Question

integral of (sin^2 (x))

Answer 1

http://www.wolframalpha.com/input/?i=int+sin%28x%29^2

Answer 2

integral, not derivative please

Answer 3

x/2-1/4 sin(2 x)+c

Answer 4

Write sin^2(x) as 1/2-1/2 cos(2 x):
= integral (1/2-1/2 cos(2 x)) dx
Integrate the sum term by term and factor out constants:
= integral 1/2 dx-1/2 integral cos(2 x) dx
For the integrand cos(2 x), substitute u = 2 x and du = 2 dx:
= integral 1/2 dx-1/4 integral cos(u) du
The integral of cos(u) is sin(u):
= integral 1/2 dx-(sin(u))/4
The integral of 1/2 is x/2:
= x/2-(sin(u))/4+constant
Substitute back for u = 2 x:
= x/2-1/4 sin(2 x)+constant
Which is equal to:
= 1/2 (x-sin(x) cos(x))+constant