<a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\int&space;\frac{1}{x^2-3x+2}&space;=\int&space;\frac{1}{(x-1)(x-2)}&space;=&space;\int&space;\frac{1}{x-2}&space;-&space;\int&space;\frac{1}{x-1}&space;=&space;\ln&space;(x-2)&space;-&space;\ln&space;(x-1)&space;+C" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\int&space;\frac{1}{x^2-3x+2}&space;=\int&space;\frac{1}{(x-1)(x-2)}&space;=&space;\int&space;\frac{1}{x-2}&space;-&space;\int&space;\frac{1}{x-1}&space;=&space;\ln&space;(x-2)&space;-&space;\ln&space;(x-1)&space;+C" title="\int \frac{1}{x^2-3x+2} =\int \frac{1}{(x-1)(x-2)} = \int \frac{1}{x-2} - \int \frac{1}{x-1} = \ln (x-2) - \ln (x-1) +C" /></a>
Also, a way to do this is note that arcsin(root(0))=0, and so this can be evaluated using the integral from 0 to a of a function of x = ab - the integral from 0 to b of the inverse function of x, where f(a)=b. I had to type this like I just did sorry haha.
you can rearrange and to simplify the inside the integrals to get<a href="https://www.codecogs.com/eqnedit.php?latex=\int&space;\frac{sinx&space;-&space;cosx}{(sinx+cosx)\sqrt{sinxcosx&space;+&space;sin^2xcos^ 2x}}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\int&space;\frac{sinx&space;-&space;cosx}{(sinx+cosx)\sqrt{sinxcosx&space;+&space;sin^2xcos^ 2x}}" title="\int \frac{sinx - cosx}{(sinx+cosx)\sqrt{sinxcosx + sin^2xcos^2x}}" /></a>
Why that reaction haha? Is there some story behind this integral?smh...
Seen it before a bit too many timesWhy that reaction haha? Is there some story behind this integral?
don't scare off the children
http://imgur.com/a/LQn6t