∫ √ cosx-cos^3x / 1-cos^3x dx is equal to

Question

\(\int \sqrt{\frac{\cos x - \cos^3 x}{1 - \cos^3 x}} dx\) is equal to

(a) \(\frac 23 \sin^{-1} (\cos ^{3/2} x) + C\)

(b) \(\frac 32 \sin^{-1} (\cos ^{3/2} x) + C\)

(c) \(\frac 23 \cos^{-1} (\cos ^{3/2} x) + C\)

(d) none of these

Answer 1

Correct option is (c) \(\frac 23 \cos^{-1} (\cos ^{3/2} x) + C\)