What is the integral of 6xe^{5x^2} ?

The integral of 6xe^{5x^2} is 3/5 e^{5x^2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 6xe^{5x^2}

\int 6 x e^{5 x^{2}} d x

\frac{3}{5} e^{5 x^{2}} + C

Solution steps

\int 6 x e^{5 x^{2}} d x

Take the constant out:

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

= 6 \cdot \int x e^{5 x^{2}} d x

Apply u-substitution

: \int \frac{e ^{u}}{10} d u

= 6 \cdot \int \frac{e ^{u}}{10} d u

Take the constant out:

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

= 6 \cdot \frac{1}{10} \cdot \int e^{u} d u

Use the common integral:

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

= 6 \cdot \frac{1}{10} e^{u}

Substitute back

u = 5 x^{2}

= 6 \cdot \frac{1}{10} e^{5 x^{2}}

Simplify

6 \cdot \frac{1}{10} e^{5 x^{2}} : \frac{3}{5} e^{5 x^{2}}

= \frac{3}{5} e^{5 x^{2}}

Add a constant to the solution

= \frac{3}{5} e^{5 x^{2}} + C

\int 6 x (x - 1) d x

\int 4 x x - 1 d x

\int \frac{1}{4 x ^{2} + 4 x + 17} d x

\int sin^{4} (x) \cdot cos^{3} (x) d x

\int \frac{ln ( 1 - x )}{e ^{2} 6 1 - x} d x

What is the integral of 6xe^{5x^2} ?
The integral of 6xe^{5x^2} is 3/5 e^{5x^2}+C