Question

Question #54da5

Answer 1

`1/2ln|sin(2x)|+C`

Explanation:

`intcot(2x)dx=intcos(2x)/sin(2x)dx`

you can easily change the numerator to equal the derivative of `sin(2x)`:
`=1/2int(2cos(2x))/sin(2x)dx=1/2int(d/dx(sin(2x)))/sin(2x)dx`

now use the rule for integration to `lnx`:
`int(f'(x))/f(x)dx=ln|f(x)|+C`

the integral becomes:
`=1/2*(ln|sin(2x)|+C)`
`=1/2ln|sin(2x)|+C` (1/2 times a constant is still a constant so the C doesn't change)