What is the integral of e^{6x}cos(6x) ?

The integral of e^{6x}cos(6x) is (e^{6x}sin(6x))/(12)+(e^{6x}cos(6x))/(12)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{6x}cos(6x)

\int e^{6 x} cos (6 x) d x

\frac{e ^{6 x} sin ( 6 x )}{12} + \frac{e ^{6 x} cos ( 6 x )}{12} + C

Solution steps

\int e^{6 x} cos (6 x) d x

Apply Integration By Parts

= \frac{1}{6} e^{6 x} sin (6 x) - \int e^{6 x} sin (6 x) d x

Apply Integration By Parts

= \frac{1}{6} e^{6 x} sin (6 x) - (- \frac{1}{6} e^{6 x} cos (6 x) - \int - e^{6 x} cos (6 x) d x)

Take the constant out:

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

= \frac{1}{6} e^{6 x} sin (6 x) - (- \frac{1}{6} e^{6 x} cos (6 x) - (- \int e^{6 x} cos (6 x) d x))

Therefore

\int e^{6 x} cos (6 x) d x = \frac{1}{6} e^{6 x} sin (6 x) - (- \frac{1}{6} e^{6 x} cos (6 x) - (- \int e^{6 x} cos (6 x) d x))

Isolate

\int e^{6 x} cos (6 x) d x

= \frac{e ^{6 x} sin ( 6 x )}{12} + \frac{e ^{6 x} cos ( 6 x )}{12}

Add a constant to the solution

= \frac{e ^{6 x} sin ( 6 x )}{12} + \frac{e ^{6 x} cos ( 6 x )}{12} + C

\int 3.17 - \frac{6.671}{x} d x

\int x sin (\frac{1}{8}) x d x

\int \frac{x - 1}{9 - x ^{2}} d x

\int \frac{x ^{4} - 6 x ^{2} + 3}{x ^{4}} d x

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

What is the integral of e^{6x}cos(6x) ?
The integral of e^{6x}cos(6x) is (e^{6x}sin(6x))/(12)+(e^{6x}cos(6x))/(12)+C