[" 14.If "I_(n)=int(sin x+cos x)^(n)dx" ,then show that "],[qquad nI_(n)=-(sin x+cos x)^(n-2)*cos2x+2(n-1)I_(n-2)" ."]

If I_(n)= int(sin nx)/(cos x)dx , then I_(n)=

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

If I_(n) = int (sin nx)/(cosx)dx , prove that I_(n)=-(2)/(n-1)cos(n-1)x-I_(n-2)

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 sin^(n)x dx , show that, I_(n)=-(1)/(n) sin^(n-1)x cosx+(n-1)/(n).I_(n-2) . Hence, evaluate, int sin^(6)x dx .

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) .