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Math Help - trig sub. intregration problem

  1. #1
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    trig sub. intregration problem

    i'm currently trying to integrate....
    e^(x)*sqrt(1-e^2x)

    i used x = sin(theta)....

    i'm just unsure what to do about the left side of the equation,i understand cos(theta) takes the place of...sqrt(1-e^2x)..but how/what takes the place of e^(x) is it just sin(theta)? -thx

    e^(x)*sqrt(1-e^2x)
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  2. #2
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    e^(i*pi)'s Avatar
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    To remove that front e^x let u = e^x \implies du = e^x dx which gives \displaystyle \int  e^x \sqrt{1-e^{2x}}\, dx = \int \sqrt{1-u^2}\, du (I have subbed in du for e^x dx)

    Then carry on with your trig sub
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by maybnxtseasn View Post
    i'm currently trying to integrate....
    e^(x)*sqrt(1-e^2x)

    i used x = sin(theta)....

    i'm just unsure what to do about the left side of the equation,i understand cos(theta) takes the place of...sqrt(1-e^2x)..but how/what takes the place of e^(x) is it just sin(theta)? -thx

    e^(x)*sqrt(1-e^2x)
    Use the substitution

    e^{x}=\sin(t) \implies e^{x}dx=\cos(t)dt

    Putting this into the integral gives

    \displaystyle \int e^{x}\sqrt{1-(e^{x})^2}dx=\int \sqrt{1-\sin^2(t)}\cos(t)dt=\int \cos^2(t)dt
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