Evaluate the indefinite integral (sin(5x)) / (1+cos^2(5x)) dx

sin5x-1cos25x-dx

#1

evaluate the indefinite integral (sin(5x)) / (1+cos^2(5x)) dx

Answer:

Let cos 5x = t now differentiate wrt x
we get
-5*sin5x dx = dt => sin5x dx = - 1/5 dt

Now question becomes –
(-1/5)(dt/1 + t^2) Now integrate we get
(-1/5)
tan^-1 t plug t = cos5x

we get

(-1/5)*tan^-1 (cos5x) + C where C is integration constant