Como você encontra a antiderivada de cos ^ 2 (x) cos2(x)?
Responda:
int cos^2(x) d x=x/2+(cos(x) sin(x))/2+C∫cos2(x)dx=x2+cos(x)sin(x)2+C
Explicação:
int cos^2(x) d x=?∫cos2(x)dx=?
"let us use the reduction formula :"let us use the reduction formula :
cos^n(x) d x=(n-1)/(n)int cos^(n-2) (x) d x+(cos^(n-1)(x) sin (x))/ncosn(x)dx=n−1n∫cosn−2(x)dx+cosn−1(x)sin(x)n
"Apply n=2"Apply n=2
int cos^2(x) d x=(2-1)/2 int cos^(2-2)(x) d x+(cos^(2-1)(x) sin(x))/2∫cos2(x)dx=2−12∫cos2−2(x)dx+cos2−1(x)sin(x)2
int cos^2(x) d x=1/2 int cos^0 (x) d x +(cos (x) sin (x))/2∫cos2(x)dx=12∫cos0(x)dx+cos(x)sin(x)2
int cos^2(x) d x=1/2 int d x+(cos (x) sin(x))/2∫cos2(x)dx=12∫dx+cos(x)sin(x)2
int cos^2(x) d x=1/2 x +(cos(x) sin(x))/2∫cos2(x)dx=12x+cos(x)sin(x)2
int cos^2(x) d x=x/2+(cos(x) sin(x))/2+C∫cos2(x)dx=x2+cos(x)sin(x)2+C