What is the integral of 3xe^{x^3-1} ?

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 3xe^{x^3-1}

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

Solution steps

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

x e^{x^{3} - 1} = e^{- 1} x e^{x^{3}}

= 3 \cdot \int e^{- 1} x e^{x^{3}} d x

Take the constant out:

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

= 3 e^{- 1} \cdot \int x e^{x^{3}} d x

Apply exponent rule:

a^{- 1} = \frac{1}{a}

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

Apply u-substitution

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

Take the constant out:

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

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

Use the nonelementary integral:

Substitute back

u = x^{2}

Add a constant to the solution