Wie finden Sie das Antiderivativ von # cos ^ 2 (x) #?

#int cos^2(x) d x=?#

#"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))/n#

#"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#

#int cos^2(x) d x=1/2 int cos^0 (x) d x +(cos (x) sin (x))/2#

#int cos^2(x) d x=1/2 int d x+(cos (x) sin(x))/2#

#int cos^2(x) d x=1/2 x +(cos(x) sin(x))/2#

#int cos^2(x) d x=x/2+(cos(x) sin(x))/2+C#