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} \cdot 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

x \to 3 - lim (- (3)^{2} + 5 (3) - 5)

8 x - 2

\int_{0}^{1} (3 e^{- x} - e^{- 2 x}) d x

y^{^{''}} + 6 y^{^{'}} + 9 y = 27 + e^{- 3 x}

\int e^{3 l n (4 x - 5)} d x

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