Mastering Integration by Parts for Complex Functions

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\int e^\sqrt[3]{x} dx

Integration by parts, perhaps? But if that's the case, I have no idea which is right value for u and which is the right one for dv... Taking ln on both sides? Uh...hmm...I don't think that's how you work this question out...

Any ideas, guys? :|

Thanks!
 
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I'm quite certain that integral in not expressible in terms of elementary functions.
 
Yeah it can... Let u^3=x
 
Last edited:
Feldoh said:
Yeah it can... Let u^3=x

Ahh my bad then. Sorry.
 
Feldoh said:
Yeah it can... Let u^3=x

OH YES. First I did that, then I used integration by parts twice to eliminate the u^2 all the way to du, then ta-daa!

Thanks!
 
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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