What is the integral of e^xsqrt(36+e^x) ?

The integral of e^xsqrt(36+e^x) is 2/3 (36+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(36+e^x)

\int e^{x} 36 + e^{x} d x

\frac{2}{3} (36 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 36 + 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 = 36 + e^{x}

= \frac{2}{3} (36 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (36 + e^{x})^{\frac{3}{2}} + C

\int \frac{t ^{2} - 9}{t ^{3}} d t

\int (\frac{1}{x ^{\frac{3}{2}}}) d x

\int 0 sin (x) d x

sec^{4} (x)

\int \frac{4 - x}{2 + x} d x

What is the integral of e^xsqrt(36+e^x) ?
The integral of e^xsqrt(36+e^x) is 2/3 (36+e^x)^{3/2}+C