What is the integral of y=(e^(13x)+sin x)/10

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

If you mean that you required the integral of y = (e^(13x)+sin x)/10, the result is.

y = (e^(13x)+sin x)/10

Int [ y dx] = Int [ (e^(13x)+sin x)/10 dx]

=> (1/10)* Int [ (e^(13x)+sin x) dx]

=> (1/10)*[ Int [ e^(13x) dx] +Int [sin x dx] ]

=> (1/10)*[ e^(13x)/13 - cos x ] + C

The integral of (e^(13x)+sin x)/10 is (1/10)*[ e^(13x)/13 - cos x ] + C

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

In other words, we'll have to calculate the indefinite integral of y.

Int [e^(13x)+sin x]dx/10 = (1/10)*[Inte^(13x)dx + Int sin x dx ]

We'll calculate each term of the sum:

Inte^(13x)dx = e^(13x)/13 + c

Int sin x dx = -cos x + c

We'll substitute the integrals by their results and we'll get:

Int [e^(13x)+sin x]dx/10 = [e^(13x)]/130 - (cos x)/10 + c

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