Integral

[man111]

[tex]\int\frac{1}{(1+x)\sqrt{1+x-x^2}}dx[/tex]

[ptj]

http://www.wolframalpha.com/input/?i=%5Cint%5Cfrac%7B1%7D%7B%281%2Bx%29%5Csqrt%7B1%2Bx-x%5E2%7D%7Ddx

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[man111]

thanks get it

Put [tex]x+1=\frac{1}{t}\Leftrightarrow dx=-\frac{1}{t^2}dt[/tex]

So [tex]-\int\frac{1}{\sqrt{-t^2+3t-1}}dt[/tex]

[tex]=-\int\frac{1}{\sqrt{\left(\frac{\sqrt{5}}{2}\right)^2-\left(t-\frac{3}{2}\right)^2}}dt[/tex]

[tex]=-\sin^{-1}\left(\frac{2t-3}{\sqrt{5}}\right)+C[/tex]

[tex]=-\sin^{-1}\left(\frac{\frac{2}{x+1}-3}{\sqrt{5}}\right)+C[/tex]