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Math`int (x+2)/(x^2+5x) dx` To solve using partial fraction method, the denominator of the integrand should be factored. `(x+2)/(x^2+5x) = (x + 2)/(x(x+5))` Then, express it as sum of fractions....

Math`int(2x^34x^215x+5)/(x^22x8)dx` The integrand is a improper rational function,as the degree of the numerator is greater than the degree of the denominator.So we have to carry out division....

Math`int(x^3x+3)/(x^2+x2)dx` The given integrand is a improper rational function, as the degree of the numerator is more than the degree of the denominator. To apply the method of partial...

Math`int (x^2+12x+12)/(x^34x)dx ` To solve using partial fraction method, the denominator of the integrand should be factored. `(x^2+12x+12)/(x^34x) =(x^2+12x+12)/(x(x2)(x+2))` Then, express it as...

Math`int(3x)/(3x^22x1)dx` Let's use partial fraction decomposition on the integrand, `(3x)/(3x^22x1)=(3x)/(3x^2+x3x1)` `=(3x)/(x(3x+1)1(3x+1))` `=(3x)/((3x+1)(x1))` Now form the partial...

Math`int 5/(x^2+3x4)dx` To solve using partial fraction, the denominator of the integrand should be factored. `5/(x^2+3x4)=5/((x+4)(x1))` Then, express it as sum of fractions....

Math`int 2/(9x^21)` To solve using partial fraction method, the denominator of the integrand should be factored. `2/(9x^21) = 2/((3x1)(3x+1))` Then, express it as sum of fractions....

Math`int 1/(x^29)dx` To solve using the partial fraction method, the first step is to factor the denominator of the integrand. `1/(x^29) =1/((x  3)(x +3))` Then, express it as a sum of two...

MathTo find the arc length of a curve, we follow the formula: `S = int_a^b sqrt(1+((dy)/(dx))^2)` if `y=f(x)` , `alt=xlt=b` or ` [a,b]` . For the given problem: `y =x^2/2` on interval `[0,4]` , we...

MathArc length of curve can be denoted as "`S` ". We can determine it by using integral formula on a closed interval [a,b] as: `S = int_a^b ds` where: `ds = sqrt(1+ ((dy)/(dx))^2 )dx` ` if y=f(x)`...

MathVolume of a shape bounded by curve `y=f(x)` and `x`axis between `a leq x leq b` revolving about `y`axis is given by `V_y=2pi int_a^b xy dx` In order to use the above formula we first need to...

MathTo find the volume of the torus generated by revolving the region bounded by the graph of circle about the yaxis, we may apply Washer method. In this method, rectangular strip representation that...

Math`intx/sqrt(x^26x+5)dx` Let's complete the square of the denominator of the integrand, `=intx/sqrt((x3)^24)dx` Now apply integral substitution:`u=x3` `=>du=1dx` `=int(u+3)/sqrt(u^22^2)du`...

MathRecall indefinite integral follows `int f(x) dx = F(x)+C` where: `f(x)` as the integrand `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration. To evaluate the given integral:...

MathRecall that indefinite integral follows `int f(x) dx = F(x) +C` where: `f(x)` as the integrand function `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration.. To evaluate the...

Math`int1/sqrt(4xx^2)dx` Complete the square for the denominator of the integrand, `=int1/sqrt((x2)^2+4)dx` Now apply integral substitution:`u=x2` `=>du=1dx` `=int1/sqrt(u^2+4)du`...

MathRecall that indefinite integral follows `int f(x) dx = F(x) +C` where: `f(x)` as the integrand function `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration. The given integral...

MathRecall that indefinite integral follows `int f(x) dx = F(x) +C` where: `f(x)` as the integrand function `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration. The given...

MathIndefinite integral are written in the form of `int f(x) dx = F(x) +C` where: `f(x)` as the integrand `F(x)` as the antiderivative function of `f(x)` `C ` as the arbitrary...

Math`int1/(4+4x^2+x^4)dx` Let's rewrite the integrand as : `=int1/((x^2)^2+2(2)(x^2)+2^2)dx` `=int1/(x^2+2)^2dx` Apply integral substitution:`x=sqrt(2)tan(u),u=arctan(x/sqrt(2))` `dx=sqrt(2)sec^2(u)du`...

MathGiven, `int sqrt(1x)/sqrt(x) dx` let us consider `u= sqrt(x)` , we can write it as `u^2 = x` Differentiating on both sides we get => `(2u)du = dx` Now let us solve the integral , `int...

MathRecall that indefinite integral follows the formula: `int f(x) dx = F(x) +C` where: `f(x)` as the integrand `F(x)` as the antiderivative function `C` as the arbitrary...

MathRecall that indefinite integral follows the formula: `int f(x) dx = F(x) +C` where: `f(x)` as the integrand `F(x)` as the antiderivative function `C` as the arbitrary...

Math`int(3x)/(x^2+3)^(3/2)dx` Take the constant out, `=3intx/(x^2+3)^(3/2)dx` Apply integral substitution:`u=x^2+3` `=>du=2xdx` `=3int1/(u)^(3/2)(du)/2` Take the constant out,...

MathRecall that indefinite integral follows the formula: `int f(x) dx = F(x) +C` where: `f(x)` as the integrand `F(x)` as the antiderivative function `C` as the arbitrary...

MathIndefinite integral are written in the form of `int f(x) dx = F(x) +C` where: `f(x)` as the integrand `F(x)` as the antiderivative function `C` as the arbitrary constant...

MathTo solve the indefinite integral, we follow `int f(x) dx = F(x) +C` where: `f(x)` as the integrand function `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration. For the given...

MathGiven , `int sqrt(1x^2)/x^4 dx` By applying Integration by parts we can solve the given integral so, let `u= sqrt(1x^2)` `,v' = (1/x^4) ` =>` u' = (sqrt(1x^2) )'` => =`d/dx (sqrt(1x^2))...

Math`int1/sqrt(x^24)dx` Let's apply integral substitution:`x=2sec(u)` `=>dx=2sec(u)tan(u)du` `=int1/sqrt((2sec(u))^24)2sec(u)tan(u)du` `=int(2sec(u)tan(u))/sqrt(4sec^2(u)4)du`...

MathGiven , `int sqrt(164x^2)dx` This Integral can be solved by using the Trigonometric substitutions (Trig substitutions) For `sqrt(abx^2)` we have to take `x=` `sqrt(a/b) sin(u)` so here , For...

MathGiven `int x^2/sqrt(36x^2) dx` This can be solved by using the Trigonometric substitutions (Trig substitutions) when the integral contains `sqrt(abx^2)` then we have to take `x=sqrt(a/b) sin(t)`...

MathGiven to solve , `int 1/sqrt(16x^2) dx` using the Trig substitutions for `sqrt(abx^2)` `x= sqrt(a/b) sin(u)` so for , `int 1/sqrt(16x^2) dx` (1) so , `x` can be `x= sqrt(16/1) sin(u)` =...

MathRecall that indefinite integral follows the formula: `int f(x) dx = F(x) +C` where:` f(x)` as the integrand `F(x)` as the antiderivative function `C` as the arbitrary...

Mathgiven to solve , `int sqrt(25x^2) dx` using the Trig Substitutions we can solve these type of integrals easily and the solution is as follows for `sqrt(abx^2) ` we can take `x= sqrt(a/b)...

MathGiven to solve, `int sqrt(4+x^2) dx` using the Trig Substitutions we can solve these type of integrals easily and the solution is as follows for `sqrt(a+bx^2) ` we can take `x= sqrt(a/b)...

MathGiven to solve, `int sqrt(9+16x^2) dx` by using the trig substitution , we can solve the integral for `sqrt(a +bx^2)` ` dx ` the `x` is given as `x= sqrt(a/b) tan(u)` so, for the integral `int...

HistoryWhen we use the term "Renaissance Man" today, we still first think of Leonardo da Vinci as the epitome of the moniker, though he lived over 500 years ago. Da Vinci created new techniques in...

HistorySectionalism arose in the United States as a response to the differences in the economies of the different regions of the United States. The North, which did not enjoy the fertile lands of the...

RikkiTikkiTaviA cantonment is a military base in India. The Kipling Society notes that the Segowlee Cantonment is a fictitious location; however, a cantonment is a real place where soldiers live and train. A...

The Scarlet LetterHester's daughter, Pearl, needs her father to acknowledge her. Until he does, she exists only as a symbol: of her parents' love, their sin, their secret, her father's guilt, her mother's scarlet...

Le Morte d'ArthurTo ascertain the difference between "good" and "bad" knights in Le Morte D'Arthur, we must look at the standard knights were measured by during Arthur's time. This standard is referred to as the...

HootRoy was born in Detroit, Michigan, but the family had moved away from there when he was just a baby, so he couldn't remember anything about Detroit. He didn't think of it as his hometown since he...

Law and PoliticsThe answer to this is “absolutely not.” A constitution is just a piece of paper. It can only be enforced on the government if the people are willing to do so. This means the government does...

The Secret Life of Walter MittyIn Walter's last daydream, he defiantly faces a firing squad, confident in his ability to die courageously. He scornfully rejects the handkerchief or blindfold, preferring to face his fate with...

The Possibility of EvilTo find examples of Miss Strangeworth being evil, look towards the end of the story when she is composing her next round of poison pen letters. Miss Strangeworth shows her darker side, for...

HistoryThe rise of Christianity in Europe during the Middle Ages led to changing views of the human body. Christianity, and more specifically Catholicism, emphasized modesty and chastity. Most artistic...

The Sun Also RisesThis question has been answered: http://www.enotes.com/homeworkhelp/hemingwayssunalsoriseswhatelementsrealism709283#answer751067

OzymandiasShelley wrote "Ozymandias" for several reasons. First, the poem was inspired by the arrival in England of a portion of a statue of the ancient Egyptian pharaoh Ramesses II. Shelley wanted to...

HistoryThe world experienced two Industrial Revolutions. The first one occurred in the mid1700s and lasted until the mid1800s. The Second Industrial Revolution occurred from around 1870 until the...

HistoryBoth the Great Awakening and the Enlightenment were eighteenthcentury movements. They were both influential throughout the British Atlantic, including Great Britain's North American colonies. They...