What is the integral of e^xsqrt(10+e^x) ?

The integral of e^xsqrt(10+e^x) is 2/3 (10+e^x)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^xsqrt(10+e^x)

\int e^{x} 10 + e^{x} d x

\frac{2}{3} (10 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 10 + e^{x} d x

Apply u-substitution

= \int u d u

Apply the Power Rule

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

Substitute back

u = 10 + e^{x}

= \frac{2}{3} (10 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (10 + e^{x})^{\frac{3}{2}} + C

\int \frac{8}{π} sin (\frac{4 x}{π}) d x

\int e^{5 x - 6} d x

\int (2 y + x) d x

\int - \frac{2}{5} x e^{- x} d x

\int (49 - x^{2})^{\frac{1}{2}} d x

What is the integral of e^xsqrt(10+e^x) ?
The integral of e^xsqrt(10+e^x) is 2/3 (10+e^x)^{3/2}+C