Problem is, I don't know what Gamma is other than a greek letter. I can use the formula, that's not the problem. I just was curious if there was a way to prove it. I was messing with my calculator and I noticed that half numbers have factorials and other decimals don't. So, I looked this up...
\int \frac {1}{x\sqrt{4x+1}}dx
Here's what I have done so far on this problem
I let u= \sqrt{4x+1} , so then u^2=4x+1 , du= \frac {2dx}{u} and x= \frac {u^2-1}{4}
Substituting, I get \int \frac {1}{(\frac{u^2-1}{4})u}du
Then moving stuff around, I get 4 \int \frac...
\int \frac {x+4}{x^2+2x+5}
I have no idea where to start on this. I can't see any substitutions that would work. I tried completing the square. I also tried to split up the fraction. It isn't getting any simpler. Any help is appreciated.
\int ln(2x+1)dx
So far I know that I need to use integration by parts, I let u= ln(2x+1) and so du= \frac {dx}{2x+1} . Also, I said dv= dx and v=x .
So then plugging this into the equation for integration I get:
xln(2x+1) - \int \frac {2x}{2x+1}dx
Then I determine that I...