Solving Inverse Trig Integral: Strategies and Tips

[kuahji]

I don't if its because I'm tired or what but I can't seem to integral the follow

$$\int (-x+1)/(x^2+1)$$ I tried substitution, u=x^2+1 du=2x, doesn't appear to be anything there, u=-x+1, du=1, again doesn't appear to be anything there. The book shows it simply as tan^-1 (x), don't think its a partial fraction. Any ideas?

 

[rocomath]

$$\int\frac{1-x}{x^2+1}dx$$

Yes?

$$\int\left(\frac{1}{x^2+1}-\frac{x}{x^2+1}\right)dx$$

How about now?

 

[kuahji]

blah, I should of seen that, thanks. :)