What is the integral of 3xe^{3x^2} ?

The integral of 3xe^{3x^2} is 1/2 e^{3x^2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3xe^{3x^2}

\int 3 x e^{3 x^{2}} d x

\frac{1}{2} e^{3 x^{2}} + C

Solution steps

\int 3 x e^{3 x^{2}} d x

Take the constant out:

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

= 3 \cdot \int x e^{3 x^{2}} d x

Apply u-substitution

: \int \frac{e ^{u}}{6} d u

= 3 \cdot \int \frac{e ^{u}}{6} d u

Take the constant out:

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

= 3 \cdot \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= 3 \cdot \frac{1}{6} e^{u}

Substitute back

u = 3 x^{2}

= 3 \cdot \frac{1}{6} e^{3 x^{2}}

Simplify

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

= \frac{1}{2} e^{3 x^{2}}

Add a constant to the solution

= \frac{1}{2} e^{3 x^{2}} + C

\int \frac{1}{1 + e ^{x}} d x

\int x (x^{2} - 12) d x

\int 16 csc^{2} (8 x) cot (8 x) d x

\int \frac{x ^{3}}{( x ^{2} - 4 ) ^{2}} d x

\int sec^{2} (5 x + 1) d x

What is the integral of 3xe^{3x^2} ?
The integral of 3xe^{3x^2} is 1/2 e^{3x^2}+C