[tex] \int\limits sin^2 {x} \, dx = \int\limits sin x sin x \, dx = \int\limits (-cos x)' sinx \, dx =[/tex]
[tex]-cosxsinx- \int\limits (-cos x) (sinx)' \, dx = -cosx sinx + \int\limits cosx *cosx \, dx [/tex]
[tex]= -cosxsinx+ \int\limits cos^2x \, dx = -cosxsinx+ \int\limits (1-sin^2x) \, dx =
[/tex]
[tex]=-cosxsinx+ \int\limits 1dx \, dx - \int\limits sin^2x \, dx = [/tex]
Notam [tex]sin^2x[/tex] cu I
[tex]-cosxsinx+x-I
I=-cosx sinx+x-I
2I=-cosx sinx + x
[/tex]
[tex]I= \frac{-cosxsinx+x}{2} +C [/tex]
[tex]Sin^2x+Cos^2x=1
Sin^2x=1-cos^2x
Cos^2x=1-Sin^2x[/tex]
