Mathematics

$$\int \dfrac{{{x^5}}}{{\sqrt {1 - {x^{12}}} }}\;dx$$


SOLUTION
$$\frac{x^{5}}{\sqrt{1-x^{12}}}dx\Rightarrow \int \frac{x^{5}}{1-(x^{6})^{2}}dx$$        $$x^{6}=t$$
$$=\frac{1}{6}\int \frac{1}{\sqrt{1-t^{2}}}dt$$         $$6x^{5}=\frac{dt}{dx}$$
$$=\frac{1}{6}sin^{-1}(t)=\frac{1}{6} sin^{-1}(x^{6})+c$$
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Subjective Medium Published on 17th 09, 2020
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