What is the integral of e^2sin(x) ?

The integral of e^2sin(x) is -e^2cos(x)+C

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integral of e^2sin(x)

\int e^{2} sin (x) d x

- e^{2} cos (x) + C

Solution steps

\int e^{2} sin (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{2} \cdot \int sin (x) d x

Use the common integral:

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

= e^{2} (- cos (x))

Simplify

= - e^{2} cos (x)

Add a constant to the solution

= - e^{2} cos (x) + C