Consider the integral. I=∫cosec5xdx The above integral is solved as I=∫cosec3x⋅cosec2xdx =cosec3x(−cotx)−∫(−cotx)3cosec2x(−cosecxcotx)dx =−cosec3xcotx−3∫cosec3xcot2xdx =−cosec3xcotx−3∫cosec5xdx+∫cosec3xdx Solve further I=−cosec3xcotx−3I+3I1 Here I1=∫cosec3xdx It is solved as I1=∫cosecx⋅cosec2xdx =−cosecxcotx−∫cosecx⋅cot2xdx =−cosecxcotx−∫cosec3xdx+∫cosecxdx =−cosecxcotx−I1+logtan