What is the integral from 0 to 1 of (x+2)e^x ?

The integral from 0 to 1 of (x+2)e^x is 2e-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of (x+2)e^x

\int_{0}^{1} (x + 2) e^{x} d x

2 e - 1

Decimal

4.43656 \dots

Solution steps

\int_{0}^{1} (x + 2) e^{x} d x

Apply Integration By Parts

: [e^{x} (x + 2) - \int e^{x} d x]_{0}^{1}

= [e^{x} (x + 2) - \int e^{x} d x]_{0}^{1}

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

= [e^{x} (x + 2) - e^{x}]_{0}^{1}

Expand

e^{x} (x + 2) - e^{x} : e^{x} x + e^{x}

= [e^{x} x + e^{x}]_{0}^{1}

Compute the boundaries:

2 e - 1

= 2 e - 1

\int_{0}^{2} \frac{3}{2} x^{2} (x - 1)^{2} d x

\int_{- π}^{π} 9 sin (x) d x

\int_{0}^{15} \frac{x}{4 + 3 x} d x

\int_{0}^{1} (8 t i + t j - k) d t

\int_{- 2}^{1} \frac{1}{( 11 + 5 x )} d x

What is the integral from 0 to 1 of (x+2)e^x ?
The integral from 0 to 1 of (x+2)e^x is 2e-1