Question

Integrate x^2.cosec x^3.cot x^3 dx, this is for 2 marks....

Answer 1

put x^3 as t

Answer 2

split up the cube terms of cosec and cot

i.e write it as cosec cot * cosec^2*cot^2, and make a subsitution, you need to get rid of x^2 by making a substitution

Answer 3

integration of cosec t cot t is just - cosec t
so final answer will be -cosec x^2+c

Answer 4

@hartnn , there are multiple ways of doing this

Answer 5

yes, i have shown the simplest......

Answer 6

@hartnn , sorry but I disagree the other may take two more steps and still get right answer

Answer 7

ok :)

Answer 8

recommend @hartnn's method, saves integration steps for few : )

Answer 9

thanx