The value of integral ∫$$dxx1$$−$$x3$$ is given equal to

Correct option is 213log⁡1−x3−11−x2+1+C

Questions

The value of integral $\int \frac{d x}{x \sqrt{1 - x^{3}}}$ is given equal to

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13log⁡1−x3+11−x3−1+C

13log⁡1−x3−11−x2+1+C

23log⁡11−x3+C

13log⁡1−x3+C

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detailed solution

Correct option is B

Put 1−x3=t2. Then −3x2dx=2tdt and the entegral becomes −13∫−3x2dxx31−x3=−13∫2tdt1−t2t=23∫dtt2−1=2312log⁡t−1t+1+C=13log⁡1−x3−11−x3+1+C.

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The value of integral ∫dxx1−x3 is given equal to

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The value of integral $\int \frac{d x}{x \sqrt{1 - x^{3}}}$ is given equal to