Integrate e^(x^1/3): Math Final Help

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I have a math final tommorow help please!

How do I integrate e^(x^1/3)

Thank you !
 
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Please show your working .

Just to get you started,
Let x^1/3 = t .
dx = 3x^(2/3)dt = 3t^2dt

Can you go from here ?
 
How did you go from dx = 3x^(2/3)dt to 3t^2dt

Ok I think I get what to do next, substiture dx into the orignal equation?
 
Last edited:
dx = 3x^{\frac{2}{3}} dt=3\left( x^{\frac{1}{3}}\right) ^{2} = 3t^2dt
 

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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