kindly check... this is an integral without using the formula of trig integrals:

solution:

from the first integral

let u = sin(5x)

du = cos(5x)dx

from the right integral u multiply both denominator and numerator by (cot(5x) + csc(5x))

let u =

du =

integrated to :

i ended up having

the answer at back of book is supposed to be:

and you shud not use a formula of trig integral