`int ((x^4 - 3x^2 + 5)/(x^4)) dx` Find the indefinite integral.

Textbook Question

Chapter 4, 4.1 - Problem 22 - Calculus of a Single Variable (10th Edition, Ron Larson).
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gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

Posted on

`int((x^4-3x^2+5)/x^4)dx`

apply the sum rule

`=intx^4/x^4dx-int(3x^2)/x^4dx+int5/x^4dx`

`=int1dx-int3x^-2dx+int5x^-4dx`

`=x-3(x^(-2+1)/(-2+1))+5(x^(-4+1)/(-4+1))`

`=x+3x^-1+5(x^-3)/(-3)`

`=x+3/x-5/(3x^3)+C`

C is constant

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scisser | (Level 3) Honors

Posted on

Simplify this by divided each term in the numerator by the denominator

`int(x^4/x^4)dx -int((3x^2)/(x^4))dx +int(5/x^4)dx`

Use the antiderivative rule: int (a^n=(a^(n+1))/(n+1))

`=x-(-3/x)-(5/(3x^3))+C`

Simplify

`=-5/(3x^3)+x+3/x+C`

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