Posted by Amy on Thursday, May 5, 2011 at 4:45am.
1.) ∫ (sin x) / (cos^2 x) dx
2.) ∫ (1) / (1+x^2) dx
3.) ∫ xe^x^2 dx
4.) ∫ x^2 sinx dx
5.) ∫ (lnx) / (x) dx

Integral Help  drwls, Thursday, May 5, 2011 at 5:50am
Most of these can be solved by the method of variable substitution. Define one function of x to be "u" and then calculate du.
For example, in #3, let u = x^2 so that
du = 2x dx. Then
ç xe^x^2 dx = (1/2)ç e^u du
= (1/2) e^u = (1/2) e^(x^2)
See how many of the others you can do with that method.
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