Step 1: Differentiate the given substitution, i.e. $u=\mathrm{f}(x)$. Step 2: Substitute the given

Question

Step 1: Differentiate the given substitution, i.e. $u=\mathrm{f}(x)$.
Step 2: Substitute the given integral in terms of $u$ and $\mathrm{d}u$.
Step 3: After integration, substitute back $x$ in.

$\displaystyle\displaystyle \displaystyle\int{\frac{\sqrt{16-{{x}^{2}}}}{{{x}^{2}}}}\mathrm{ d}x,$ let $x=4\sin \theta$

Accepted Answer

$-\frac{\sqrt{16-x^2}}{x}-\sin^{-1}\left(\frac{x}{4}\right)+C$

Techniques of Integration - Integration by Substitution

Techniques of Integration - Integration by Substitution

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