Integral Troubleshooting: e^[(y^2)/2 + lny] | Calc Homework

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Homework Statement


integrate e^[(y^2)/2 + lny]


Homework Equations





The Attempt at a Solution


i think we learned this in either calc 2 or calc 1 but i can't remember how to do this one. any help would be appreciated
 
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e^(a+b)=e^a*e^b. e^(ln(y))=y. Use those to simplify the integral. Now do a u substitution.
 
ooooo ok that was a little easier htan i thought, thanks!
 

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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