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

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

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integral of sin(e^x)e^x

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

- cos (e^{x}) + C

Solution steps

\int sin (e^{x}) 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 y}{d x} = \frac{3 y ^{2} + 10 x ^{2}}{x y}

\frac{d}{d x} (7 x - 5)

\int_{0}^{4} x^{\frac{3}{2}} d x

\int_{1}^{5} \frac{5}{x} - \frac{3}{x ^{2}} d x

x \to - 2 lim (- x^{2} + 8 x - 7)

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