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

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

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integral of e^x(sin(e^x))

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

- cos (e^{x}) + C

Solution steps

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

= - cos (e^{x})

Add a constant to the solution

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

\frac{d}{d x} (- 4 cos^{2} (x))

n = 1 \sum \infty \frac{e}{π}

p (h) = 30 e^{- 0.0000323 h}

\int_{0}^{5} \frac{x - 3}{x ^{2} - 5 x - 6} d x

\frac{\partial}{\partial x} (sin (x) ln (x^{4} + \frac{1}{x}))

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