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Math Help - Integration help when n&m are both the same

  1. #1
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    Integration help when n&m are both the same

    I need help with solving the integral of:
    cos^3(x)sin^3(x)dx

    I got:
    (1/4)sin^4(x)-(1/5)sin^5(x)+c as the answer but I don't think it's correct...

    I tried to use the table of integrals I have but I couldn't find something that met that scenario so I ended up substituting u for sin(x) as well as du for cos(x) and had the following before substituting u back in, I used the trig. property of cos^2(x) = 1-sin^2(x):
    Integral of u^3(1-u^2)du

    Then:
    Integral of (u^3-u^5)du

    Thanks,
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  2. #2
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    Hello,
    Quote Originally Posted by Pi314 View Post
    I need help with solving the integral of:
    cos^3(x)sin^3(x)dx

    I got:
    (1/4)sin^4(x)-(1/5)sin^5(x)+c as the answer but I don't think it's correct...

    I tried to use the table of integrals I have but I couldn't find something that met that scenario so I ended up substituting u for sin(x) as well as du for cos(x) and had the following before substituting u back in, I used the trig. property of cos^2(x) = 1-sin^2(x):
    Integral of u^3(1-u^2)du

    Then:
    Integral of (u^3-u^5)du

    Thanks,
    Your substitution is correct

    But there is a problem for the integration.

    \int u^5 ~du=\frac{u^6}{6}+c
    and you wrote \frac{\sin^5(x)}{5}
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  3. #3
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    Wow, I can't believe I didn't spot that.

    Thanks.
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