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 \infty lim (\frac{1}{x} - 4)

f (x) = \frac{1 + x}{1 + e ^{x}}, at x = 0

\frac{10}{s ( s + 3 )}

2 x^{2} - 6 x

x \to 2 + lim (∣ x + 2 ∣ - 2)

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