What is the integral of e^xsqrt(11+e^x) ?

The integral of e^xsqrt(11+e^x) is 2/3 (11+e^x)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^xsqrt(11+e^x)

\int e^{x} 11 + e^{x} d x

\frac{2}{3} (11 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 11 + e^{x} d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 11 + e^{x}

= \frac{2}{3} (11 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (11 + e^{x})^{\frac{3}{2}} + C

104 - 80 e^{- 0.2 t}

arcsin (2 x + 1)

\int e^{(- \frac{x ^{2}}{4})} d x

\frac{d y}{d t} = \frac{t}{y - 2}

\int cot (x) csc (x) d x

What is the integral of e^xsqrt(11+e^x) ?
The integral of e^xsqrt(11+e^x) is 2/3 (11+e^x)^{3/2}+C