What is the integral of e^xsqrt(5-e^x) ?

The integral of e^xsqrt(5-e^x) is -2/3 (5-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(5-e^x)

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

- \frac{2}{3} (5 - e^{x})^{\frac{3}{2}} + C

Solution steps

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

Apply u-substitution

= \int - u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u d u

Apply the Power Rule

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

Substitute back

u = 5 - e^{x}

= - \frac{2}{3} (5 - e^{x})^{\frac{3}{2}}

Add a constant to the solution

= - \frac{2}{3} (5 - e^{x})^{\frac{3}{2}} + C

What is the integral of e^xsqrt(5-e^x) ?
The integral of e^xsqrt(5-e^x) is -2/3 (5-e^x)^{3/2}+C