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Thread: Integration

  1. #1
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    Integration

    $\displaystyle \int 3\mathrm{sec}^3x\tan x \ \mathrm{d}x$

    Thanks in advance.
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  2. #2
    MHF Contributor red_dog's Avatar
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    $\displaystyle \int 3\sec^3x\tan xdx=3\int \frac{\sin x}{\cos^4x}dx$.
    Use the substitution $\displaystyle \cos x=u$
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Air View Post
    $\displaystyle \int 3\mathrm{sec}^3x\tan x \ \mathrm{d}x$

    Thanks in advance.
    Alternatively we have
    $\displaystyle 3\int\sec^2(x)\cdot\sec(x)\tan(x)dx$
    Let $\displaystyle u=\sec(x)\Rightarrow{du=\sec(x)\tan(x)}$

    Giving us

    $\displaystyle 3\int{u^2du}$
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