What is the integral of-(e^xsin(x))/2 ?

The integral of-(e^xsin(x))/2 is -1/4 (-e^xcos(x)+e^xsin(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-(e^xsin(x))/2

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

- \frac{1}{4} (- e^{x} cos (x) + e^{x} sin (x)) + C

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

Therefore

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

Isolate

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

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

Simplify

- \frac{1}{2} (- \frac{e ^{x} cos ( x )}{2} + \frac{e ^{x} sin ( x )}{2}) : - \frac{1}{4} (- e^{x} cos (x) + e^{x} sin (x))

= - \frac{1}{4} (- e^{x} cos (x) + e^{x} sin (x))

Add a constant to the solution

= - \frac{1}{4} (- e^{x} cos (x) + e^{x} sin (x)) + C

\int 30 - 10 x d x

\frac{d y}{d x} - y = 9 x

y^{^{'''}} - y^{^{'}} = 0

f (x) e^{- (x - 2)^{2}} + 3

\int sin^{3} (φ) d φ

What is the integral of-(e^xsin(x))/2 ?
The integral of-(e^xsin(x))/2 is -1/4 (-e^xcos(x)+e^xsin(x))+C