What is the integral of 15xe^{x^2} ?

The integral of 15xe^{x^2} is 15/2 e^{x^2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 15xe^{x^2}

\int 15 x e^{x^{2}} d x

\frac{15}{2} e^{x^{2}} + C

Solution steps

\int 15 x e^{x^{2}} d x

Take the constant out:

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

= 15 \cdot \int x e^{x^{2}} d x

Apply u-substitution

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

= 15 \cdot \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

= 15 \cdot \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= 15 \cdot \frac{1}{2} e^{u}

Substitute back

u = x^{2}

= 15 \cdot \frac{1}{2} e^{x^{2}}

Simplify

15 \cdot \frac{1}{2} e^{x^{2}} : \frac{15}{2} e^{x^{2}}

= \frac{15}{2} e^{x^{2}}

Add a constant to the solution

= \frac{15}{2} e^{x^{2}} + C

\frac{d}{d x} (ln (\frac{2 x}{x + 9}))

x \to 0 - lim (x + 1)

b

sin (x), cos (x), 0, π

\int \frac{2 ^{x + 1} - 5 ^{x - 1}}{1 0 ^{x}} d x

What is the integral of 15xe^{x^2} ?
The integral of 15xe^{x^2} is 15/2 e^{x^2}+C