∫cosec3x⋅cosec2xdx=I By applying integration by parts I=−cotxcosec3x+∫cotx(−3cosec2xcotxcosecx)dx I=−cotxcosec3x−3∫cosec3x(cosec2x−1)dx I=−cotxcosec3x−3I+3∫cosec3xdx let I1=∫cosec3xdx=−cosecxcotx−∫cot2xcosecxdx I1=−cosecxcotx−∫(cosec2x−1)cosecxdx 2I1=−cosecxcotx+ln|tan