What is the integral of e^xsqrt(25+e^x) ?

The integral of e^xsqrt(25+e^x) is 2/3 (25+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(25+e^x)

\int e^{x} 25 + e^{x} d x

\frac{2}{3} (25 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 25 + 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 = 25 + e^{x}

= \frac{2}{3} (25 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (25 + e^{x})^{\frac{3}{2}} + C

\frac{d y}{d x} = \frac{x ^{2} + y ^{2}}{2 x y}

\frac{d}{d x} (cot (x) - sin (2 x))

y = x, x^{2}, [0, 1]

y = - \frac{8 x}{x ^{2} + 1}, (1, - 4)

x^{2} + 2 x + 11, - 4 x + 2, x = 0

What is the integral of e^xsqrt(25+e^x) ?
The integral of e^xsqrt(25+e^x) is 2/3 (25+e^x)^{3/2}+C