What is the integral of x^3e^{5x^2} ?

The integral of x^3e^{5x^2} is 1/50 (e^{5x^2}*5x^2-e^{5x^2})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^3e^{5x^2}

\int x^{3} e^{5 x^{2}} d x

\frac{1}{50} (e^{5 x^{2}} \cdot 5 x^{2} - e^{5 x^{2}}) + C

Solution steps

\int x^{3} e^{5 x^{2}} d x

Apply u-substitution

: \int \frac{e ^{u} u}{50} d u

= \int \frac{e ^{u} u}{50} d u

Take the constant out:

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

= \frac{1}{50} \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= \frac{1}{50} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{50} (e^{u} u - e^{u})

Substitute back

u = 5 x^{2}

= \frac{1}{50} (e^{5 x^{2}} \cdot 5 x^{2} - e^{5 x^{2}})

Add a constant to the solution

= \frac{1}{50} (e^{5 x^{2}} \cdot 5 x^{2} - e^{5 x^{2}}) + C

\int \frac{x ^{3}}{25 - x ^{4}} d x

\int \frac{( x + 7 ) ^{5}}{2 x} d x

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

\int - 3^{x} d x

sin (x^{3})

What is the integral of x^3e^{5x^2} ?
The integral of x^3e^{5x^2} is 1/50 (e^{5x^2}*5x^2-e^{5x^2})+C