en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xe^{5x^2+9}

Solution

\int x e^{5 x^{2} + 9} d x

Solution

\frac{1}{10} e^{5 x^{2} + 9} + C

Solution steps

\int x e^{5 x^{2} + 9} d x

Apply u-substitution

: \int \frac{e ^{u}}{10} d u

= \int \frac{e ^{u}}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{10} e^{u}

Substitute back

u = 5 x^{2} + 9

= \frac{1}{10} e^{5 x^{2} + 9}

Add a constant to the solution

= \frac{1}{10} e^{5 x^{2} + 9} + C

Popular Examples

integral of 5/(x(x+1)^2)

\int \frac{5}{x ( x + 1 ) ^{2}} d x

integral of 50-3xe^{0.01x^2}

\int 50 - 3 x e^{0.01 x^{2}} d x

integral of (21t^2-10t)/(7t^3-5t^2+13)

\int \frac{21 t ^{2} - 10 t}{7 t ^{3} - 5 t ^{2} + 13} d t

integral of (x^2+2)/(sqrt(x^3+6x))

\int \frac{x ^{2} + 2}{x ^{3} + 6 x} d x

integral of sin^5(v)cos^2(v)

\int sin^{5} (v) cos^{2} (v) d v

Frequently Asked Questions (FAQ)

What is the integral of xe^{5x^2+9} ?
The integral of xe^{5x^2+9} is 1/10 e^{5x^2+9}+C