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Thread: Integration problem

  1. #1
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    Integration problem

    $\displaystyle
    \[\int tan^3(x) sec^4(x) dx\]
    $

    I first tried substituting $\displaystyle \[u = tan(x)\]$, then I tried substituting $\displaystyle \[u = sec(x)\]$, but I couldn't seem to solve it.

    Any hints?
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  2. #2
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    Quote Originally Posted by BrownianMan View Post
    $\displaystyle
    \[\int tan^3(x) sec^4(x) dx\]
    $

    I first tried substituting $\displaystyle \[u = tan(x)\]$, then I tried substituting $\displaystyle \[u = sec(x)\]$, but I couldn't seem to solve it.

    Any hints?
    $\displaystyle \int tan^3(x)sec^4(x)$ cab be written as

    $\displaystyle \int tan^3(x)sec^2(x)sec^2(x)$

    $\displaystyle \int tan^3(x)[1 + tan^2(x)]sec^2(x)$

    Now simplify and solve.
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  3. #3
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    $\displaystyle tan^2(x)+1=sec^2(x)$
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  4. #4
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    Thank you!
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