What is the integral of e^{(x^2)/2}*x ?

The integral of e^{(x^2)/2}*x is e^{(x^2)/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{(x^2)/2}*x

\int e^{\frac{x ^{2}}{2}} \cdot x d x

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

Solution steps

\int e^{\frac{x ^{2}}{2}} x d x

Apply u-substitution

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

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

Apply u-substitution

: \int e^{v} \cdot 2 d v

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} \cdot 2 e^{v}

Substitute back

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

Simplify

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

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

Add a constant to the solution

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

\int x e^{\frac{2}{x}} d x

\int e^{7 x} \cdot sin (2 x) d x

\int 35 csc (5 x) sec (5 x) d x

\int \frac{18 x}{x ^{2} + 1} d x

\int (- \frac{A R x ^{2}}{2} + C) d x

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