What is the integral of e^xsqrt(17+e^x) ?

The integral of e^xsqrt(17+e^x) is 2/3 (17+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(17+e^x)

\int e^{x} 17 + e^{x} d x

\frac{2}{3} (17 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 17 + 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 = 17 + e^{x}

= \frac{2}{3} (17 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (17 + e^{x})^{\frac{3}{2}} + C

What is the integral of e^xsqrt(17+e^x) ?
The integral of e^xsqrt(17+e^x) is 2/3 (17+e^x)^{3/2}+C