Mathematics

Solve: $$\displaystyle\int \dfrac{x^3}{\sqrt{x^4 + 1}}dx$$


SOLUTION
Now,
$$\displaystyle\int \dfrac{x^3}{\sqrt{x^4 + 1}}dx$$
$$=\dfrac{1}{4}\displaystyle\int \dfrac{4x^3}{\sqrt{x^4 + 1}}dx$$
$$=\dfrac{1}{4}\displaystyle\int \dfrac{d(x^4+1)}{\sqrt{x^4 + 1}}dx$$
$$=\dfrac{1}{4}.2\sqrt{x^4+1}+c$$ [ Where $$c$$ is integrating constant]
$$=\dfrac{1}{2}\sqrt{x^4+1}+c$$
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Subjective Medium Published on 17th 09, 2020
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