What is the integral of 5e^{4x}cos(x) ?

The integral of 5e^{4x}cos(x) is 5((e^{4x}sin(x))/(17)+(4e^{4x}cos(x))/(17))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5e^{4x}cos(x)

\int 5 e^{4 x} cos (x) d x

5 (\frac{e ^{4 x} sin ( x )}{17} + \frac{4 e ^{4 x} cos ( x )}{17}) + C

Solution steps

\int 5 e^{4 x} cos (x) d x

Take the constant out:

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

= 5 \cdot \int e^{4 x} cos (x) d x

Apply Integration By Parts

: e^{4 x} sin (x) - \int e^{4 x} \cdot 4 sin (x) d x

= 5 (e^{4 x} sin (x) - \int e^{4 x} \cdot 4 sin (x) d x)

Take the constant out:

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

= 5 (e^{4 x} sin (x) - 4 \cdot \int e^{4 x} sin (x) d x)

Apply Integration By Parts

: - e^{4 x} cos (x) - \int - 4 e^{4 x} cos (x) d x

= 5 (e^{4 x} sin (x) - 4 (- e^{4 x} cos (x) - \int - 4 e^{4 x} cos (x) d x))

Take the constant out:

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

= 5 (e^{4 x} sin (x) - 4 (- e^{4 x} cos (x) - (- 4 \cdot \int e^{4 x} cos (x) d x)))

Therefore

5 \cdot \int e^{4 x} cos (x) d x = 5 (e^{4 x} sin (x) - 4 (- e^{4 x} cos (x) - (- 4 \cdot \int e^{4 x} cos (x) d x)))

Isolate

\int e^{4 x} cos (x) d x

= 5 (\frac{e ^{4 x} sin ( x )}{17} + \frac{4 e ^{4 x} cos ( x )}{17})

Add a constant to the solution

= 5 (\frac{e ^{4 x} sin ( x )}{17} + \frac{4 e ^{4 x} cos ( x )}{17}) + C

\int \frac{8 x ^{2}}{100 - x ^{2}} d x

\int \frac{x + 8}{x ^{2} + x + 2} d x

\int e^{- t} 2 t e^{2 t} d t

\int \frac{x ^{2}}{( 7 + x ^{3} ) ^{2}} d x

\int \frac{x ^{3} + 4}{x ^{5} + 14 x ^{3} + 40 x} d x

What is the integral of 5e^{4x}cos(x) ?
The integral of 5e^{4x}cos(x) is 5((e^{4x}sin(x))/(17)+(4e^{4x}cos(x))/(17))+C