[14/,int sin mx sin nxdx[m^(2)!=n^(2)]],[,=(1)/(2)[(sin(m-n)x)/(m-n)-(sin(m+n)x)/(m+n)]+c]

Prove : int sin mx sin n x dx[ m^(2) != n^(2)] , = 1/2 [ (sin(m-n)x)/(m-n) - (sin (m+n)x)/(m+n) ] + c

int sin mx cos nxdx,m!=n

int cos mx cos nxdx,m!=n

Integrate: int sin mx cos nxdx,m!=n

If intsin^(4)x cos^(3)xdx=(1)/(m)sin^(m)x-(1)/(n)sin^(n)x+c then (m,n)-=

If m, n in N , then int_(0)^(pi//2)((sin^(m)x)^(1/n))/((sin^(m)x)^(1/n)+(cos^(m)x)^(1/n))dx is equal to

If m, n in N , then int_(0)^(pi//2)((sin^(m)x)^(1/n))/((sin^(m)x)^(1/n)+(cos^(m)x)^(1/n))dx is equal to

((sin^(m)x)/(sin^(n)x))^(m+n)*((sin^(n)x)/(sin^(q)x))^(n+q)((sin^(q)x)/(sin^(m)x))^(q+m)

If I_(m,n)=int cos^(m)x sin nxdx=f(m,n)I_(m-1)-(cos^(m)x cos nx)/(m+n), then f(m,n)=

If quad ((sin^(m)x)/(sin^(n)x))^(m+n)((sin^(n)x)/(sin^(p)x))^(n+p)((sin^(p)x)/(sin^(m)x))^(p+) then f(x) is equal to