Let `I=int_(0)sqrt((1+x)(1+x^(3)))dx,` then `

int_0^1 sqrt((1-x)/(1+x)) dx

If I=int_(0)^(1) (dx)/(sqrt(1+x^(4)))dx then

If I=int_(0)^(1) (1)/(1+x^(pi//2))dx then

Let I = int_(1)^(3)sqrt(x^(4)+x^(2)) , dx then

Let I= int_(0)^(1) (e^(x))/( x+1) dx, then the vlaue of the intergral int_(0)^(1) (xe^(x^(2)))/( x^(2)+1) dx, is

Let I_(n) = int_(0)^(1)(1-x^(3))^(n)dx, (nin N) then

Let I_(1)=int_(0)^(oo)(x^(2)sqrtx)/((1+x)^(6))dx,I_(2)=int_(0)^(oo)(xsqrtx)/((1+x)^(6))dx , then

int_(0)^(1) (x)/(sqrt(1 + x^(2))) dx

int_(0)^(1) (1)/(sqrt(1-x^(2)))dx

Let I_(n)=int_(0)^(1)x^(n)sqrt(1-x^(2))dx. Then lim_(nrarroo)(I_(n))/(I_(n-2))=