What is the integral of 2x^3e^{3x^4} ?

The integral of 2x^3e^{3x^4} is 1/6 e^{3x^4}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2x^3e^{3x^4}

\int 2 x^{3} e^{3 x^{4}} d x

\frac{1}{6} e^{3 x^{4}} + C

Solution steps

\int 2 x^{3} e^{3 x^{4}} d x

Take the constant out:

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

= 2 \cdot \int x^{3} e^{3 x^{4}} d x

Apply u-substitution

: \int \frac{e ^{3 u^{\frac{4}{3}}} u ^{\frac{1}{3}}}{3} d u

= 2 \cdot \int \frac{e ^{3 u^{\frac{4}{3}}} u ^{\frac{1}{3}}}{3} d u

Take the constant out:

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

= 2 \cdot \frac{1}{3} \cdot \int e^{3 u^{\frac{4}{3}}} u^{\frac{1}{3}} d u

Apply u-substitution

: \int \frac{3 e ^{3 v}}{4} d v

= 2 \cdot \frac{1}{3} \cdot \int \frac{3 e ^{3 v}}{4} d v

Take the constant out:

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

= 2 \cdot \frac{1}{3} \cdot \frac{3}{4} \cdot \int e^{3 v} d v

Apply u-substitution

: \int e^{w} \frac{1}{3} d w

= 2 \cdot \frac{1}{3} \cdot \frac{3}{4} \cdot \int e^{w} \frac{1}{3} d w

Take the constant out:

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

= 2 \cdot \frac{1}{3} \cdot \frac{3}{4} \cdot \frac{1}{3} \cdot \int e^{w} d w

Use the common integral:

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

= 2 \cdot \frac{1}{3} \cdot \frac{3}{4} \cdot \frac{1}{3} e^{w}

Substitute back

= 2 \cdot \frac{1}{3} \cdot \frac{3}{4} \cdot \frac{1}{3} e^{3 (x^{3})^{\frac{4}{3}}}

Simplify

2 \cdot \frac{1}{3} \cdot \frac{3}{4} \cdot \frac{1}{3} e^{3 (x^{3})^{\frac{4}{3}}} : \frac{1}{6} e^{3 x^{4}}

= \frac{1}{6} e^{3 x^{4}}

Add a constant to the solution

= \frac{1}{6} e^{3 x^{4}} + C

\int_{1}^{2} x^{2} + 2 x d x

\int_{0}^{π} sin (5 x) d x

y = (x^{3} - 16 x)^{12}

5 x - 2 x^{2}

x \to - 5 - lim (\frac{x + 5}{x + 5})

What is the integral of 2x^3e^{3x^4} ?
The integral of 2x^3e^{3x^4} is 1/6 e^{3x^4}+C