What is the integral from 1 to 3 of x^3e^x ?

The integral from 1 to 3 of x^3e^x is 12e^3+2e

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 3 of x^3e^x

\int_{1}^{3} x^{3} e^{x} d x

12 e^{3} + 2 e

Decimal

246.46300 \dots

Solution steps

\int_{1}^{3} x^{3} e^{x} d x

Apply Integration By Parts

: [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{1}^{3}

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{1}^{3}

\int 3 x^{2} e^{x} d x = 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

= [x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))]_{1}^{3}

Compute the boundaries:

12 e^{3} + 2 e

= 12 e^{3} + 2 e

\int_{0}^{1} 3 t^{3} d t

\int_{- 3}^{2} 3 x^{2} d x

\int_{- 1}^{2} (3 x - 1 x^{1}) d x

\int_{0}^{\frac{π}{2}} \frac{1 - cos ( 2 t )}{2} d t

\int_{0}^{6} \frac{36 - x ^{2}}{144} d x

What is the integral from 1 to 3 of x^3e^x ?
The integral from 1 to 3 of x^3e^x is 12e^3+2e