What is the integral of 10xe^{2x} ?

The integral of 10xe^{2x} is 5e^{2x}x-5/2 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 10xe^{2x}

\int 10 x e^{2 x} d x

5 e^{2 x} x - \frac{5}{2} e^{2 x} + C

Solution steps

\int 10 x e^{2 x} d x

Take the constant out:

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

= 10 \cdot \int x e^{2 x} d x

Apply u-substitution

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

= 10 \cdot \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

= 10 \cdot \frac{1}{4} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= 10 \cdot \frac{1}{4} (e^{u} u - \int e^{u} d u)

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

= 10 \cdot \frac{1}{4} (e^{u} u - e^{u})

Substitute back

u = 2 x

= 10 \cdot \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})

Simplify

10 \cdot \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}) : 5 e^{2 x} x - \frac{5}{2} e^{2 x}

= 5 e^{2 x} x - \frac{5}{2} e^{2 x}

Add a constant to the solution

= 5 e^{2 x} x - \frac{5}{2} e^{2 x} + C

\int \frac{cos ( x )}{sin ^{2} ( x ) + 4} d x

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

x^{2} + 1

\int \frac{6}{3 x} d x

\int \frac{1}{1 + v} d v

What is the integral of 10xe^{2x} ?
The integral of 10xe^{2x} is 5e^{2x}x-5/2 e^{2x}+C