What is the integral of e^xsin(e^x+7) ?

The integral of e^xsin(e^x+7) is -cos(e^x+7)+C

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integral of e^xsin(e^x+7)

\int e^{x} sin (e^{x} + 7) d x

- cos (e^{x} + 7) + C

Solution steps

\int e^{x} sin (e^{x} + 7) d x

Apply u-substitution

: \int sin (u) d u

= \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= - cos (u)

Substitute back

u = e^{x} + 7

= - cos (e^{x} + 7)

Add a constant to the solution

= - cos (e^{x} + 7) + C

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What is the integral of e^xsin(e^x+7) ?
The integral of e^xsin(e^x+7) is -cos(e^x+7)+C