Integrate the function in Exercise: x^ 3 1-x^ 8 - Vidyadip

Question

Integrate the function in Exercise:
$\frac{\text{x}^{3}}{\sqrt{1-\text{x}^{8}}}$

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Answer

$\frac{\text{x}^{3}}{\sqrt{1-\text{x}^{8}}}$ $\text{Let}\ \text{x}^{4}=\text{t}\Rightarrow4\text{x}^{3}\text{dx}=\text{dt}$ $\Rightarrow\int\frac{\text{x}^{3}}{\sqrt{1-\text{x}^{8}}}\text{dx}=\frac{1}{4}\int\frac{\text{dt}}{\sqrt{1-\text{t}^{2}}}$ $=\frac{1}{4}\sin^{-1}\text{t}+\text{C}$$=\frac{1}{4}\sin^{-1}\text{(x}^{4})+\text{C}$

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