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

The integral of e^{5x}cos(5x) is (e^{5x}sin(5x))/(10)+(e^{5x}cos(5x))/(10)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{e ^{5 x} sin ( 5 x )}{10} + \frac{e ^{5 x} cos ( 5 x )}{10} + C

Solution steps

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

Apply Integration By Parts

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

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

Apply Integration By Parts

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

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

Therefore

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

Isolate

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

= \frac{e ^{5 x} sin ( 5 x )}{10} + \frac{e ^{5 x} cos ( 5 x )}{10}

Add a constant to the solution

= \frac{e ^{5 x} sin ( 5 x )}{10} + \frac{e ^{5 x} cos ( 5 x )}{10} + C

\int x^{2} - 16 x d x

t^{2} + 6 t - 3

f (x) = 3 - 4 x^{2}, - 61, at x = 4

n = 1 \sum \infty arctan (n)

\int 2 x^{3} + 4 d x

What is the integral of e^{5x}cos(5x) ?
The integral of e^{5x}cos(5x) is (e^{5x}sin(5x))/(10)+(e^{5x}cos(5x))/(10)+C