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Math Help - integration

  1. #1
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    integration

    Integrate:

    2xe^(x^2)

    AND

    sinx/(2+cosx)

    If anyone could help me with these two integrals it would be greatly appreciated, thank you !
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  2. #2
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    Quote Originally Posted by christina View Post
    Integrate:

    2xe^(x^2)

    AND

    sinx/(2+cosx)

    If anyone could help me with these two integrals it would be greatly appreciated, thank you !

    Hints: for the first one, \int f'(x)f(x)\,dx=\frac{f(x)^2}{2}+C(onstant)

    For the second one, \int\frac{f'(x)}{f(x)}dx=\ln|f(x)|+C(onstant)

    Tonio
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  3. #3
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    Quote Originally Posted by christina View Post
    Integrate:

    2xe^(x^2) Mr F says: Substitute u = x^2.

    AND

    sinx/(2+cosx) Mr F says: Substitute u = 2 + cos x.

    If anyone could help me with these two integrals it would be greatly appreciated, thank you !
    ..
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  4. #4
    Senior Member Shanks's Avatar
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    \int 2xe^{x^2}dx=\int e^{x^2}dx^2=e^{x^2}+C.
    similarly for the second one.
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  5. #5
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    In other words, for the first one use the substitution u= x^2 and for the second, u= 2+ cos(x).
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