How do you integrate 3ye^3z dz using u substitution?

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Homework Statement



Needing to integrate 3ye^3z dz

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The Attempt at a Solution


I believe you use u substitution and u=3z du=3dz
Then you get yze^3z. Is this correct?
 
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If you differentiate yze3z with respect to z do you get what you started with? I don't think so, but can you fix it?
 
>>Then you get yze^3z. Is this correct?
No completely, you have an extra factor of z
 
I believe differentiating ye^3z with respect to z will give 3ye^3z. Therefore, integrating 3ye^3z dz will be ye^3z. Correct?
 
Yes.
 
Sweet,thanks to the both of you
 

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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