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

The integral of sin(e^x)e^{2x} is -e^xcos(e^x)+sin(e^x)+C

Popular >

integral of sin(e^x)e^{2x}

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

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

Solution steps

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

Apply u-substitution

: \int u sin (u) d u

= \int u sin (u) d u

Apply Integration By Parts

: - u cos (u) - \int - cos (u) d u

= - u cos (u) - \int - cos (u) d u

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

= - u cos (u) - (- sin (u))

Substitute back

u = e^{x}

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

Simplify

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

Add a constant to the solution

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

\frac{3}{( s + 1 ) ^{4}}

x \to 1 lim (4)

\frac{d x}{d t} + 5 t^{3} x^{5} + \frac{x}{t} = 0

\frac{d}{d x} ((2 - x^{2}) (4 x^{2} + 9 x)^{4})

\frac{d}{d x} (\frac{5 ^{x}}{x ^{5}})

What is the integral of sin(e^x)e^{2x} ?
The integral of sin(e^x)e^{2x} is -e^xcos(e^x)+sin(e^x)+C