Question

integrala din sinus patrat de x totul la patrat . va roggg

Answer 1

cos 2x= cos²x-sin²x= 2cos²x-1= 1-2sin²x
=> cos²x= (1+cos2x)/2
si sin²x= (1-cos2x)/2

int (sin²x)² dx= int [1-cos2x)/2]² dx=int 1/4 (1-2cos2x+cos²2x) dx=
= 1/4 [(x- sin2x) + int (1+cos4x)/2 dx]=  
= 1/4 [x-sin2x + 1/2 (x +sin4x/4)] +C= 3/4x -1/4 sin2x +1/8 sin4x +C