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

The integral of e^{-x}sin^2(x) is -e^{-x}sin^2(x)-2/5 e^{-x}cos(2x)-1/5 e^{-x}sin(2x)+C

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

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

- e^{- x} sin^{2} (x) - \frac{2}{5} e^{- x} cos (2 x) - \frac{1}{5} e^{- x} sin (2 x) + C

Solution steps

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

Apply Integration By Parts

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

\int - e^{- x} sin (2 x) d x = \frac{2}{5} e^{- x} cos (2 x) + \frac{1}{5} e^{- x} sin (2 x)

= - e^{- x} sin^{2} (x) - (\frac{2}{5} e^{- x} cos (2 x) + \frac{1}{5} e^{- x} sin (2 x))

Simplify

= - e^{- x} sin^{2} (x) - \frac{2}{5} e^{- x} cos (2 x) - \frac{1}{5} e^{- x} sin (2 x)

Add a constant to the solution

= - e^{- x} sin^{2} (x) - \frac{2}{5} e^{- x} cos (2 x) - \frac{1}{5} e^{- x} sin (2 x) + C

\frac{d x}{d t} = \frac{4 x}{t}, x (1) = 1

t an g e n t \frac{4 x}{x + 1}

\int_{1}^{1.5} (\frac{1}{8} + \frac{3}{8} x) d x

x \to - \infty lim (x^{1})

\int_{0}^{π} 11 sin^{2} (2 x) d x

What is the integral of e^{-x}sin^2(x) ?
The integral of e^{-x}sin^2(x) is -e^{-x}sin^2(x)-2/5 e^{-x}cos(2x)-1/5 e^{-x}sin(2x)+C