What is the integral of e^{2x}x ?

The integral of e^{2x}x is 1/4 (e^{2x}*2x-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 e^{2x}x

\int e^{2 x} x d x

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

Solution steps

\int e^{2 x} x d x

Apply u-substitution

: \int \frac{e ^{u} u}{4} d u

= \int \frac{e ^{u} u}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= \frac{1}{4} (e^{u} u - \int e^{u} d u)

\int e^{u} d u = e^{u}

= \frac{1}{4} (e^{u} u - e^{u})

Substitute back

u = 2 x

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

Add a constant to the solution

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

\int 9 x^{2} - 24 x - 36 d x

\frac{d}{d x} (cos (1 - 4 x))

f (x) = \frac{3 - ( \frac{1}{x ^{2}} )}{x + 4}

\int e^{- s t} cos (t) d t

t y^{^{'}} = 2

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