[tex]\int \frac{3\sqrt{x^2-16}}{2x}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Let [tex]x = 4\sec\theta[/tex], [tex]dx = 4\sec\theta\tan\theta d\theta[/tex]. [tex]\theta = asec(x/4)[/tex]

[tex]\frac{3}{2}\int \frac{\sqrt{4^2(\sec^2\theta-1)}}{4\sec\theta}4\sec\theta\tan\theta d\theta[/tex]

[tex]\frac{3}{2}\int \frac{\sqrt{\tan^2\theta}}{\sec\theta}4\sec\theta\tan\theta d\theta[/tex]

[tex]\frac{4\times 3}{2}\int \tan^2\theta d\theta[/tex]

as [tex]tan^2 = sec^2-1[/tex]

[tex]6\int sec^2 d\theta - 6\int d\theta[/tex]

[tex]6 \tan\theta - 6\theta[/tex]

As [tex]\tan\theta = \frac{\sqrt{x^2-16}}{4}[/tex]

[tex]6 \tan\theta - 6\theta = \frac{3}{2}\sqrt{x^2-16} - 6 arcsec\left(\frac{x}{4}\right) + C[/tex]

I don't know what's wrong but when I plot it on graphmatica and derive it, it doesn't match with the original equation.

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# What's wrong with my integral ?

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