What is the integral of e^θsin(θ) ?

The integral of e^θsin(θ) is -(e^θcos(θ))/2+(e^θsin(θ))/2+C

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integral of e^θsin(θ)

\int e^{θ} sin (θ) d θ

- \frac{e ^{θ} cos ( θ )}{2} + \frac{e ^{θ} sin ( θ )}{2} + C

Solution steps

\int e^{θ} sin (θ) d θ

Apply Integration By Parts

: - e^{θ} cos (θ) - \int - e^{θ} cos (θ) d θ

= - e^{θ} cos (θ) - \int - e^{θ} cos (θ) d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - e^{θ} cos (θ) - (- \int e^{θ} cos (θ) d θ)

Apply Integration By Parts

: e^{θ} sin (θ) - \int e^{θ} sin (θ) d θ

= - e^{θ} cos (θ) - (- (e^{θ} sin (θ) - \int e^{θ} sin (θ) d θ))

Therefore

\int e^{θ} sin (θ) d θ = - e^{θ} cos (θ) - (- (e^{θ} sin (θ) - \int e^{θ} sin (θ) d θ))

Isolate

\int e^{θ} sin (θ) d θ

= - \frac{e ^{θ} cos ( θ )}{2} + \frac{e ^{θ} sin ( θ )}{2}

Add a constant to the solution

= - \frac{e ^{θ} cos ( θ )}{2} + \frac{e ^{θ} sin ( θ )}{2} + C

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

n = 1 \sum \infty \frac{( ( - 3 ) ^{n - 1} )}{5 ^{n}}

f (x) = 4 (x - 4)^{2} (x - 1)

\frac{\partial}{\partial y} (x y e^{x z})

\int 2 sin^{3} (x) d x

What is the integral of e^θsin(θ) ?
The integral of e^θsin(θ) is -(e^θcos(θ))/2+(e^θsin(θ))/2+C