What is the integral of e^xsqrt(1+e^x) ?

The integral of e^xsqrt(1+e^x) is 2/3 (1+e^x)^{3/2}+C

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integral of e^xsqrt(1+e^x)

\int e^{x} 1 + e^{x} d x

\frac{2}{3} (1 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 1 + 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 = 1 + e^{x}

= \frac{2}{3} (1 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (1 + e^{x})^{\frac{3}{2}} + C

\frac{A}{y ^{10}} + B e^{y}

y = x + 1, y = x^{2} - 1

\int \frac{x ^{2} - x + 30}{x ^{3} + 5 x} d x

\frac{\partial}{\partial x} (cos (w + x) sin (y - z))

\frac{d}{d t} (3 t - 2)

What is the integral of e^xsqrt(1+e^x) ?
The integral of e^xsqrt(1+e^x) is 2/3 (1+e^x)^{3/2}+C