What is the integral of e^xsqrt(4+e^x) ?

The integral of e^xsqrt(4+e^x) is 2/3 (4+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(4+e^x)

\int e^{x} 4 + e^{x} d x

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

Solution steps

\int e^{x} 4 + 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 = 4 + e^{x}

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

Add a constant to the solution

= \frac{2}{3} (4 + e^{x})^{\frac{3}{2}} + C

\frac{\partial}{\partial x} (2 y e^{x})

6 + 5 x^{2} - 2 x^{3}

\int \frac{x ^{2} - 5 x - 6}{x ^{2} - 4} d x

\int 8 e^{9 x} d x

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 0

What is the integral of e^xsqrt(4+e^x) ?
The integral of e^xsqrt(4+e^x) is 2/3 (4+e^x)^{3/2}+C