What is the integral of e^{9x}cos(5x) ?

The integral of e^{9x}cos(5x) is (5e^{9x}sin(5x))/(106)+(9e^{9x}cos(5x))/(106)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{9x}cos(5x)

\int e^{9 x} cos (5 x) d x

\frac{5 e ^{9 x} sin ( 5 x )}{106} + \frac{9 e ^{9 x} cos ( 5 x )}{106} + C

Solution steps

\int e^{9 x} cos (5 x) d x

Apply Integration By Parts

: \frac{1}{5} e^{9 x} sin (5 x) - \int \frac{9}{5} e^{9 x} sin (5 x) d x

= \frac{1}{5} e^{9 x} sin (5 x) - \int \frac{9}{5} e^{9 x} sin (5 x) d x

Take the constant out:

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

= \frac{1}{5} e^{9 x} sin (5 x) - \frac{9}{5} \cdot \int e^{9 x} sin (5 x) d x

Apply Integration By Parts

: - \frac{1}{5} e^{9 x} cos (5 x) - \int - \frac{9}{5} e^{9 x} cos (5 x) d x

= \frac{1}{5} e^{9 x} sin (5 x) - \frac{9}{5} (- \frac{1}{5} e^{9 x} cos (5 x) - \int - \frac{9}{5} e^{9 x} cos (5 x) d x)

Take the constant out:

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

= \frac{1}{5} e^{9 x} sin (5 x) - \frac{9}{5} (- \frac{1}{5} e^{9 x} cos (5 x) - (- \frac{9}{5} \cdot \int e^{9 x} cos (5 x) d x))

Therefore

\int e^{9 x} cos (5 x) d x = \frac{1}{5} e^{9 x} sin (5 x) - \frac{9}{5} (- \frac{1}{5} e^{9 x} cos (5 x) - (- \frac{9}{5} \cdot \int e^{9 x} cos (5 x) d x))

Isolate

\int e^{9 x} cos (5 x) d x

= \frac{5 e ^{9 x} sin ( 5 x )}{106} + \frac{9 e ^{9 x} cos ( 5 x )}{106}

Add a constant to the solution

= \frac{5 e ^{9 x} sin ( 5 x )}{106} + \frac{9 e ^{9 x} cos ( 5 x )}{106} + C

y = - x^{3} + 2 x

sin (\frac{π}{6} + x)

\frac{d}{d x} (1 - e^{- 4 x})

\int 1^{\frac{1}{2}}

\frac{- x ^{2} - 4 x}{( x ^{2} - x - 2 ) ^{2}}

What is the integral of e^{9x}cos(5x) ?
The integral of e^{9x}cos(5x) is (5e^{9x}sin(5x))/(106)+(9e^{9x}cos(5x))/(106)+C