Integral Help

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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 -

    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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