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Math Help - please help determine the following integrals

  1. #1
    Junior Member
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    please help determine the following integrals

    \int (3x-1)(x+2)dx

    b) \int cos(7x+2)dx

    c) \int \frac {y}{\sqrt {1+2y^2}} dy

    d) \int \frac {sin2x}{1+sin^2x}dx

    e) \int_{0}^\frac{\pi}{2}{sin2xcosx} dx

    f) \int [\ln{4} - \frac {1}{\ln(e^{2x})}]dx
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  2. #2
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    Quote Originally Posted by joey1 View Post
    \int (3x-1)(x+2)dx

    b) \int cos(7x+2)dx

    c) \int \frac {y}{\sqrt {1+2y^2}} dy

    d) \int \frac {sin2x}{1+sin^2x}dx

    e) \int_{0}^\frac{\pi}{2}{sin2xcosx} dx

    f) \int [\ln{4} - \frac {1}{\ln(e^{2x})}]dx
    (a) : Expand.
    (b) & (c) : Use a substitution.
    (d) & (e) : Rewrite sin(2x) as 2sin(x)cos(x), then use a substitution.
    (f) : Recall that : \int ( \, f(x) - g(x) \, ) \, dx = \int f(x) \, dx \, - \int g(x) \, dx .. and Note that ln(e^{f(x)}) = f(x).

    Also, post only two question in each thread.
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