Show that
If `I _(n) =int cos ^(n) x dx,` then show that
`I_(n) =1/n cos ^(n-1) x sin x + (n-1)/(n ) I_(n-2).`

If I_(n)=int cos^(n)x dx . Prove that I_(n)=(1)/(n)(cos^(n-1)x sinx)+((n-1)/(n))I_(n-2) .

Evaluate: If int cos^(n)xdxdot provethatI_(n)=(1)/(n)(cos^(n-1)x sin x)+((n-1)/(x))I_(n)

If I_(n)=int cos^(n)xdx, then (n+1)I_(n+1)-nI_(n-1)=

If I_(n)=int x^(n)cos axdx and I_(n)=int x^(n)sin axdx then show that.(1)aI_(n)=x^(n)sin ax-nI_(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_(n)=int cos^(n)xdx, then I_(7)-(cos^(6)x sin x)/(7)=

int x ^ (2n-1) cos x ^ (n) dx

If l_(n)=int e^(mx)cos^(n)xdx then prove that (m^(2)+n^(2))I_(n)=e^(mx)*(m cos x+n sin x)cos^(n-1)x+n(n-1)l_(n)

If I_(n)=int_(0)^(pi/2) sin^(x)x dx , then show that I_(n)=((n-1)n)I_(n-2) . Hence prove that I_(n)={(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(1/2)(pi)/2,"if",n"is even"),(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(2/3)1,"if",n"is odd"):}

If I_(n)=int(sin nx)/(sin x)dx, for n>1, then the value of I_(n)-I_(n-2) is