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Evaluate the integral: `int sin(9x)*e^cos(9x)dx`

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dawks | Student, Undergraduate | (Level 1) Honors

Posted March 23, 2012 at 2:07 PM via web

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Evaluate the integral: `int sin(9x)*e^cos(9x)dx`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 23, 2012 at 2:43 PM (Answer #1)

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The integral `int (sin 9x)*e^(cos 9x) dx` has to be evaluated.

`int (sin 9x)*e^(cos 9x) dx`

let cos 9x = y

`(-1/9)*dy = sin 9x dx`

=> `int (-1/9) e^y dy`

=>` -e^y/9`

substitute y = cos 9x

=>` -e^(cos 9x)/9`

The required integral is `-e^(cos 9x)/9 + C`

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