Right choice is (c) –\([\frac{cot^4(x)}{4}+\frac{cot^6(x)}{6}]\)
Easy explanation: Add constant automatically
Given, \(\int cot^3(x)cosec^4 (x)dx=-\int cot^3(x)cosec^2 (x)dcot(x)\)
=-\(\int t^3 (1+t^2)dt=-[\frac{t^4}{4}+\frac{t^6}{6}]=-[\frac{cot^4(x)}{4}+\frac{cot^6(x)}{6}]\)