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Math Help - A Couple Integral Problems I'm Stuck On

  1. #1
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    A Couple Integral Problems I'm Stuck On

    Hey, hope you are all well this fine evening


    I've been working on some homework problems for tomorrow, and I am absolutely stuck on two of them.

    1) integral of (1+sinx) / (1-sinx)

    For this one, I couldn't come up with any trig identities that would help. I thought about squaring the numerator and denominator but I have no idea if you can do that for integrals haha. Hopefully you guys would know hehe

    2) integral of ((x^5)(e^(-x^3))

    For this one, I tried integration by parts but ended up with a larger exponent somewhere down the road, so I figured I was just thinking about it incorrectly. And I can't do the tabular method because I can't integrate e^(-x^3)). My next guess was u-substitution but I'm just not seeing how to apply it.

    The book says that these are all "elementary functions" so no series needed. I think I'm just dumb haha. Any help would be awesome. Thanks guys
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  2. #2
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    Quote Originally Posted by coolguy9 View Post
    Hey, hope you are all well this fine evening


    I've been working on some homework problems for tomorrow, and I am absolutely stuck on two of them.

    1) integral of (1+sinx) / (1-sinx)

    For this one, I couldn't come up with any trig identities that would help. I thought about squaring the numerator and denominator but I have no idea if you can do that for integrals haha. Hopefully you guys would know hehe

    2) integral of ((x^5)(e^(-x^3))

    For this one, I tried integration by parts but ended up with a larger exponent somewhere down the road, so I figured I was just thinking about it incorrectly. And I can't do the tabular method because I can't integrate e^(-x^3)). My next guess was u-substitution but I'm just not seeing how to apply it.

    The book says that these are all "elementary functions" so no series needed. I think I'm just dumb haha. Any help would be awesome. Thanks guys
    #1 multiply top and bottom by \frac{1+ \sin x}{1 + \sin x} and use and identity on the bottom.

    #2, try the substitution u = -x^3
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  3. #3
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    \frac{1+\sin{x}}{1-\sin{x}} \cdot \frac{1+\sin{x}}{1+\sin{x}} =<br />

    \frac{1 + 2\sin{x} + \sin^2{x}}{1 -\sin^2{x}} =<br />

    \frac{1 + 2\sin{x} + \sin^2{x}}{\cos^2{x}} =

    \sec^2{x} + 2\sec{x}\tan{x} + \tan^2{x} =

    2\sec^2{x} + 2\sec{x}\tan{x} - 1

    last expression should be easy to integrate.


    x^5 \cdot e^{-x^3} =

    x^3 \cdot x^2 \cdot e^{-x^3}

    let t = x^3 ... dt = 3x^2 \, dx

    \frac{1}{3} \int t \cdot e^{-t} \, dt

    now use tabular.
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  4. #4
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    Ah, you guys are life savers. Thanks to the both of you

    In regards to the u = -x^3, I just didn't see to split up the x^5. Bad miss on my part hehe

    Anyways, thanks again
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