Question

`int color(white)(.) sin(x^2)` ?

Answer 1

`int sin^2 """x"" " dx=x/2-(sin 2x)/4 + C`

Explanation:

The question is not so clear.

Just in case it means,

Integrate `(sin x)^2`, then

From Half-Angle Formulas in Trigonometry,

`sin^2 x=1/2-1/2cos 2x`

Integration part

`int sin^2 """x"" " dx=int (1/2-1/2cos 2x)dx`

`int sin^2 """x"" " dx=int (1/2)dx-1/2int(cos 2x)dx`

`int sin^2 """x"" " dx=int (1/2)dx-1/((2)(2))int(cos 2x)2dx`

`int sin^2 """x"" " dx=1/2x-1/4sin 2x+C`

I hope the explanation is useful.....God bless...