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Question

Mathematics Question on Integration

∫1x31−1x2dx=\int\frac{1}{x^3}\sqrt{1-\frac{1}{x^2}}dx=

A

−16(1−1x2)32+C\frac{-1}{6}(1-\frac{1}{x^2})^{\frac{3}{2}}+C

B

13(1−1x2)32+C\frac{1}{3}(1-\frac{1}{x^2})^{\frac{3}{2}}+C

C

−13(1−1x2)32+C\frac{-1}{3}(1-\frac{1}{x^2})^{\frac{3}{2}}+C

D

43(1−1x2)32+C\frac{4}{3}(1-\frac{1}{x^2})^{\frac{3}{2}}+C

E

−43(1−1x2)32+C\frac{-4}{3}(1-\frac{1}{x^2})^{\frac{3}{2}}+C

Answer

13(1−1x2)32+C\frac{1}{3}(1-\frac{1}{x^2})^{\frac{3}{2}}+C

Explanation

Solution

The correct option is (B) : 13(1−1x2)32+C\frac{1}{3}(1-\frac{1}{x^2})^{\frac{3}{2}}+C