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Math Help - intergrating

  1. #1
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    intergrating

    please can anyone solve the following problems for me and show me step by step working please


    1)integral(x^2 (e^5)^x, dx)

    2)[IMG]file:///C:/Users/Taichi/AppData/Local/Temp/moz-screenshot-2.jpg[/IMG]integral(4 x/sqrt(8 x^2-1), dx, 1, 2)


    3)integral((x^3-2 x^2-4 x-4)/(x^2+x-2), x)


    Thanks in advance

    Tiachi[IMG]file:///C:/Users/Taichi/AppData/Local/Temp/moz-screenshot-1.jpg[/IMG]
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  2. #2
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    Quote Originally Posted by taichi2910 View Post
    please can anyone solve the following problems for me and show me step by step working please


    1)integral(x^2 (e^5)^x, dx)

    2)[IMG]file:///C:/Users/Taichi/AppData/Local/Temp/moz-screenshot-2.jpg[/IMG]integral(4 x/sqrt(8 x^2-1), dx, 1, 2)


    3)integral((x^3-2 x^2-4 x-4)/(x^2+x-2), x)


    Thanks in advance


    Tiachi[IMG]file:///C:/Users/Taichi/AppData/Local/Temp/moz-screenshot-1.jpg[/IMG]
    Sorry but we don't give any step by step solutions unless you've shown you've attempted them.

    1) Notice that (e^5)^x = e^{5x}.

    So the integral becomes \int{x^2e^{5x}\,dx}.

    Use Integration by Parts.


    2) Rewrite as \int_1^2{4x(8x^2 -1)^{-\frac{1}{2}}\,dx}

    Use a u-substitution with u = 8x^2 - 1.


    3) Long divide first.
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