en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2e^{x^3+1}

Solution

\int x^{2} e^{x^{3} + 1} d x

Solution

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

Solution steps

\int x^{2} e^{x^{3} + 1} d x

Apply u-substitution

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

= \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

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

Use the common integral:

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

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

Substitute back

u = x^{3} + 1

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

Add a constant to the solution

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

Popular Examples

integral of 1/(16x^2+9)

\int \frac{1}{16 x ^{2} + 9} d x

integral of ((x^3+4))/(x^2+4)

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

integral of 2e^{4x}

\int 2 e^{4 x} d x

inverse oflaplace 5/(3(s+3)^2+27)inverse laplace

\frac{5}{3 ( s + 3 ) ^{2} + 27}

limit as x approaches-1 of x/(x-1)

x \to - 1 lim (\frac{x}{x - 1})

Frequently Asked Questions (FAQ)

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