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

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

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

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

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

Solution steps

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

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

Add a constant to the solution

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

x \to 6 lim (x^{2} - 3 x)

\int (\frac{1}{x - 1}) d x

\frac{\partial}{\partial x} (e^{y} \cdot sin (x))

y^{^{''}} + 12 x = 0, y (0) = - 4, y^{^{'}} (0) = 5

\frac{\partial}{\partial x} (\frac{6 y}{x + y})

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