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

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

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integral of e^xsin(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

\int 5 sin^{5} (x) cos^{3} (x) d x

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

x \to - 1 lim (\frac{2 x + 1}{x - 2})

x^{2} + 3 x, at x = 0

\int - 5 ln (x^{2} - 1) d x

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