What is the integral of x*e^{x^2-1} ?

The integral of x*e^{x^2-1} is 1/2 e^{x^2-1}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x*e^{x^2-1}

\int x \cdot e^{x^{2} - 1} d x

\frac{1}{2} e^{x^{2} - 1} + C

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} e^{u}

Substitute back

u = x^{2} - 1

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

Add a constant to the solution

= \frac{1}{2} e^{x^{2} - 1} + C

\int sec^{2} (t) tan^{7} (t) d t

\int sin (x) (1 + cos (x)) d x

\int \frac{1}{x ^{2}} cosh (\frac{1}{x}) d x

\int \frac{1}{1 - x ^{2} arcsin ^{3} ( x )} d x

\int \frac{4 x + 3}{x ^{2} + 4 x + 8} d x

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