Trig substitution.. Please HELP !

[qzack96]

I really needed some help with these trig substitution problems. Please write the u and du values for each. I'd really really appreciate it !

1) Integrate [x/(sq(x^2 +1))] dx

2) Integrate [dx/(1+x^2)]

3) Integrate [arctanx/(1+x^2)] dx


Thank you Again !!!

 

[BigGlenntheHeavy]

\(\displaystyle \int\frac{x}{\sqrt(x^{2}+1)}dx, \ Let \ u \ = \ x^{2}+1, \ then \ du \ = \ 2xdx.\)

\(\displaystyle \int\frac{dx}{1+x^{2}}, \ let \ x \ = \ tan\theta, \ then \ dx \ = \ sec^{2}\theta d\theta.\)

\(\displaystyle \int \frac{arctan(x)}{1+x^{2}}dx, \ Let \ u \ = \ arctan(x), \ then \ du \ = \ \frac{dx}{1+x^{2}}.\)

 

[fasteddie65]

The solution to the second problem is simply "arctan x + C", because d(arctan x) = dx/(1 + x^2).