What is the integral of ((xe^{2x}))/((1+2x)^2) ?

The integral of ((xe^{2x}))/((1+2x)^2) is -(e^{2x}x)/(2(1+2x))+1/4 e^{2x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((xe^{2x}))/((1+2x)^2)

\int \frac{( x e ^{2 x} )}{( 1 + 2 x ) ^{2}} d x

- \frac{e ^{2 x} x}{2 ( 1 + 2 x )} + \frac{1}{4} e^{2 x} + C

Solution steps

\int \frac{x e ^{2 x}}{( 1 + 2 x ) ^{2}} d x

Apply Integration By Parts

: - \frac{e ^{2 x} x}{2 ( 1 + 2 x )} - \int - \frac{1}{2} e^{2 x} d x

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

\int - \frac{1}{2} e^{2 x} d x = - \frac{1}{4} e^{2 x}

= - \frac{e ^{2 x} x}{2 ( 1 + 2 x )} - (- \frac{1}{4} e^{2 x})

Simplify

= - \frac{e ^{2 x} x}{2 ( 1 + 2 x )} + \frac{1}{4} e^{2 x}

Add a constant to the solution

= - \frac{e ^{2 x} x}{2 ( 1 + 2 x )} + \frac{1}{4} e^{2 x} + C

f (x) = \frac{1}{x}, at x = - 2

\frac{d}{d x} (\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x)

\frac{d}{d x} (2 e^{x^{2}})

\frac{\partial}{\partial x} ((x + y) e^{x})

\int \frac{1}{P} d P

What is the integral of ((xe^{2x}))/((1+2x)^2) ?
The integral of ((xe^{2x}))/((1+2x)^2) is -(e^{2x}x)/(2(1+2x))+1/4 e^{2x}+C