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Question Number 124624 by bemath last updated on 04/Dec/20

$$\int \frac{dx}{\sqrt[3]{x}+4x}$$

Answered by Dwaipayan Shikari last updated on 04/Dec/20

$$\int \frac{3u^{2}du}{u+4u^3}=\frac{3}{8}\int \frac{8udu}{1+4u^2}=\frac{3}{8}log(1+4u^2)=\frac{3}{8}log(1+4x^{\frac{2}{3}})+C$$$$Taking(x=u^3)$$

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