What is the integral from 1/2 to 3 of e^{sqrt(2x+3)} ?

The integral from 1/2 to 3 of e^{sqrt(2x+3)} is 2e^3-e^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1/2 to 3 of e^{sqrt(2x+3)}

\int_{\frac{1}{2}}^{3} e^{2 x + 3} d x

2 e^{3} - e^{2}

Decimal

32.78201 \dots

Solution steps

\int_{\frac{1}{2}}^{3} e^{2 x + 3} d x

Apply u-substitution

: \int_{2}^{3} e^{u} u d u

= \int_{2}^{3} e^{u} u d u

Apply Integration By Parts

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

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

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

= [e^{u} u - e^{u}]_{2}^{3}

Compute the boundaries:

2 e^{3} - e^{2}

= 2 e^{3} - e^{2}

\int_{- 4}^{- 1} x^{2} (3 - 4 x) d x

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

\int_{1}^{3 x} (x^{3} e^{x y}) d y

\int_{1}^{4} 1 + \frac{1}{u} + \frac{1}{u ^{2}} d u

\int_{x}^{x^{3}} e^{t^{2}} d t

What is the integral from 1/2 to 3 of e^{sqrt(2x+3)} ?
The integral from 1/2 to 3 of e^{sqrt(2x+3)} is 2e^3-e^2