Can anyone can help me ?

[rainyrainy906]

\(\displaystyle \mbox{a) }\, \displaystyle{ \int\, \sqrt[3]{e^x\, -\, 1\, }\, dx }\)

\(\displaystyle \mbox{b) }\, \displaystyle{ \int\, \frac{\left(x^2\, +\, x\right)\, e^x}{x\, +\, e^{-x}}\, dx }\)

\(\displaystyle \mbox{c) }\, \displaystyle{ \int\, \frac{xe^x\, +\, 1}{x\left(e^x \, +\, \ln(x)\right)}\, dx }\)

Thank you

 

[Deleted member 4993]

\(\displaystyle \mbox{a) }\, \displaystyle{ \int\, \sqrt[3]{e^x\, -\, 1\, }\, dx }\)

\(\displaystyle \mbox{b) }\, \displaystyle{ \int\, \frac{\left(x^2\, +\, x\right)\, e^x}{x\, +\, e^{-x}}\, dx }\)

\(\displaystyle \mbox{c) }\, \displaystyle{ \int\, \frac{xe^x\, +\, 1}{x\left(e^x \, +\, \ln(x)\right)}\, dx }\)

Thank you :grin:

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Hint for 1)

substitute

e^x - 1 = u³

3u²du = e^xdx

dx = 3u²/(u³ + 1) du ..... and continue....