`(n(n+1))/(n-1)int (cosx)^(n-1)/(sinx)^(n+1)dx`

int(x^(n-1))/(sqrt(1+4x^(n)))dx

int(2x^(n-1))/(x^(n)+3)dx

int(1)/(x(x^(n)+1))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) .

The value of (^nC_(0))/(n)+(^nC_(1))/(n+1)+(^nC_(2))/(n+2)+....+(n)/(2n) is equal to a.int_(0)^(1)x^(n-1)(1-x)^(n)dxbint_(1)^(2)x^(n)(x-1)^(n-1)dxc*int_(1)^(2)x^(n-1)(1+x)^(n)dx d.int_(0)^(1)(1-x)^(n-1)dx

Prove that for ngt1 . int_0^1(cos^-1x)^ndx=n(pi/2)^(n-1)-n(n-1)int_0^1(cos^-1x)^(n-2)dx

(b) int(x^(n-1)dx)/(sqrt(a^n+x^n))

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

If I_(n)=int(sinx+cosx)^(n) dx, snd I_(n)=1/n(sinx+cosx)^(n-1)(sinx-cosx)+(2k)/(n) I_(n-2) then k=