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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