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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int \frac{e ^{u^{\frac{3}{2}}} u}{2 x} d u

= - 2 \cdot \int \frac{e ^{u}}{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^{u} d u

Use the common integral:

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

= - 2 \cdot \frac{1}{3} e^{u}

Substitute back

u = x^{3}

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{3 x ^{2} - 7 x}{3 x + 2} d x

\int \frac{e ^{- \frac{1}{x ^{2}}}}{x ^{3}} d x

\int 2 + 3 x d x

\int \frac{cos ( x + 1 )}{x + 1} d x

\int x arcsin (\frac{1}{x}) d x

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