What is the integral of e^xsqrt(15+e^x) ?

The integral of e^xsqrt(15+e^x) is 2/3 (15+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(15+e^x)

\int e^{x} 15 + e^{x} d x

\frac{2}{3} (15 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 15 + 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 = 15 + e^{x}

= \frac{2}{3} (15 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (15 + e^{x})^{\frac{3}{2}} + C

\frac{d}{d x} (\frac{3}{8} (x^{\frac{4}{3}} - 2 x^{\frac{2}{3}}))

\frac{d}{d x} (- sin (5 π x) \cdot 5 π)

\frac{d}{d x} ((x^{3} + 2)^{2} (x^{4} + 4)^{4})

y^{^{'}} (t) = 0.3 y \cdot (1 - \frac{y}{2500}) - \frac{y}{4}, y (0) = 600

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

What is the integral of e^xsqrt(15+e^x) ?
The integral of e^xsqrt(15+e^x) is 2/3 (15+e^x)^{3/2}+C