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Math Help - Calculus help please!!!

  1. #1
    Newbie
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    Dec 2008
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    Calculus help please!!!

    I don't even know where to start on these... please show steps so I can try to learn this stuff...

    1. ∫ x (x +3)^9 dx

    2.
    ∫ x
    ------- *dx
    (x
    +7)^5


    3. sec(x)^15 tan(x) dx


    Thank you so much!


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  2. #2
    Newbie
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    Dec 2008
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    2 came out wrong, its: x / (x^2 + 7)^5
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  3. #3
    Junior Member Ziaris's Avatar
    Joined
    Dec 2008
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    1. \int x^2 (x^3+9)^9 dx. Use substitution, u=x^3+9. So du = 3x^2dx, dx = \frac{du}{3x^2} and resubstituting back in,

    \int x^2 (x^3+9)^9 dx=\frac{1}{3}\int u^9du=\frac{u^{10}}{30}+C=\frac{(x^3+9)^{10}}{30}+  C.

    2. \int \frac{x}{(x^2+7)^5}dx. Substitute u=x^2+7.

    3. \int \sec^{15} x \tan x\;dx. Substitute  u = \sec x.
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