How Do You Solve the Integral of e^x * sqrt(1+e^x) dx?

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Homework Statement



Integral e^{}x\sqrt{}1+e^{}x dx

Homework Equations


using the formula: integral e^x dx:e^x+C

The Attempt at a Solution


I tried basic substitution:
making u=sqrt 1+e^x, and when trying to find du I'm not sure on what to do next
 
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Just try u=(1+e^x). I think you'll find it goes more simply.
 
jimen113 said:

Homework Statement



Integral e^{}x\sqrt{}1+e^{}x dx
Do you mean
\int e^x\sqrt{1+ e^x}dx

If so just u= 1+ ex is sufficient.

(Put your "x" inside the "{ }" in tex!

Homework Equations


using the formula: integral e^x dx:e^x+C

The Attempt at a Solution


I tried basic substitution:
making u=sqrt 1+e^x, and when trying to find du I'm not sure on what to do next[/QUOTE]
 
thanks!
 
Solved:
2/3 sqrt(1+e^x)^3
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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