If `I_(m)=int (sin x+cos x)^(m)dx`, then show that `m l_(m)=(sin x+ cos x)^(m-1)*(sin x- cos x)+2(m-1) I_(m-2)`

If I_(m.n) = int sin^(m) x cos^(n) xdx then I_(5,4) =

int(sin^(m)x)/(cos^(m+2)x)dx=

If I_(m,n) = int cos^m x cdot cos nx cdot dx show that (m + n) I_(m,n) = cos^m x cdot sin nx + m I_(m - 1, n-1)

If I_(m;n)=int_(0)^((pi)/(2))sin^(m)x cos^(n)xdx then show that I_(m;n)=(m-1)/(m+n)I_(m-2;n) and find I_(m;n) in terms of different combinations of m and n.

sin^(m)x.cos^(n)x

If I_(m"," n)=int cos^(m)x*cos nx dx , show that (m+n)I_(m","n)=cos^(m)x*sin nx+m I_((m-1","n-1))

If I_(m"," n)=int cos^(m)x*cos nx dx , show that (m+n)I_(m","n)=cos^(m)x*sin nx+m I_((m-1","n-1))

If I_(m"," n)=int cos^(m)x*cos nx dx , show that (m+n)I_(m","n)=cos^(m)x*sin nx+m I_((m-1","n-1))

If I(m)=int_(0)^( pi)ln(1-2m cos x+m^(2))dx then I(1)=