Solving Substitution Problem: \int (x2 +2x +1)e^(-ln(x+1)) dx

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Homework Statement



\int (x2 +2x +1)e^(-ln(x+1)) dx


Homework Equations






The Attempt at a Solution



I started off by factoring the integrand into:

\int (x+1)(x+1)e^(-ln(x+1)) du

Then I tried to make a substitution:

u=(x+1) so du=dx

This left me with this:

\int u2 e^(-lnu) du

So now do I use integration by parts or something? Thanks in advance for the help. And also, if someone responds to my question and I want to respond back, do I just reply to this same thread or PM the person who responded? I ask this because I don't know if I were to reply to this thread if the person will be notified or not. Thanks again.
 
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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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