What is the integral of-8x^2e^{x^3} ?

The integral of-8x^2e^{x^3} is -8/3 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-8x^2e^{x^3}

\int - 8 x^{2} e^{x^{3}} d x

- \frac{8}{3} e^{x^{3}} + C

Solution steps

\int - 8 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

= - 8 \cdot \int x^{2} e^{x^{3}} d x

Apply u-substitution

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

= - 8 \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

= - 8 \cdot \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= - 8 \cdot \frac{1}{3} e^{u}

Substitute back

u = x^{3}

= - 8 \cdot \frac{1}{3} e^{x^{3}}

Simplify

- 8 \cdot \frac{1}{3} e^{x^{3}} : - \frac{8}{3} e^{x^{3}}

= - \frac{8}{3} e^{x^{3}}

Add a constant to the solution

= - \frac{8}{3} e^{x^{3}} + C

\int 0.02 x d x

\int x (x^{2} + 1)^{8} d x

\int w 1 - w d w

\int θ^{2} cos (2 θ) d θ

\int \frac{2}{y ^{3}} d y

What is the integral of-8x^2e^{x^3} ?
The integral of-8x^2e^{x^3} is -8/3 e^{x^3}+C