int_(0)^(4)(x^(2))/(1+x)dx

Evaluate the integrals : I = int_(0)^(pi//4) (x^(2))/( x^(2) + 1) dx ,

If int_(0)^(1)f(x)dx=1, int_(0)^(1)x f(x)dx=a and int_(0)^(1)x^(2)f(x)dx=a^(2) , then : int_(0)^(1)(a-x)^(2)f(x)dx=

If A=int_(0)^(1)(e^(x))/(x+1)dx then int_(0)^(1)(x^(2)e^(x))/(x+1)dx=

If I_(1)=int_(0)^(2)(x^(2))/([x^(2)-4x+4]+[x^(2)])dx and I_(2)=int_(0)^(2)(4)/([x^(2)-4x]+[x^(2)-4])dx then I_(1)-I_(2)=

Let u=int_(0)^(oo)(dx)/(x^(4)+7x^(2)+1) and v=int_(0)^(x)(x^(2)dx)/(x^(4)+7x^(2)+1) then

If int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx , then

If I_(1)=int_(0)^(1) 2^(x^(2)) dx, I_(2)=int_(0)^(1) 2^(x^(3)) dx, I_(3)=int_(1)^(2) 2^(x^(2))dx and I_(4)=int_(1)^(2) 2^(x^(2))dx then

If I_(1)=int_(0)^(1) 2^(x^(2)) dx, I_(2)=int_(0)^(1) 2^(x^(3)) dx, I_(3)=int_(1)^(2) 2^(x^(2))dx and I_(4)=int_(1)^(2) 2^(x^(3))dx then

If int_(0)^(1)(sin x)/(1+x)dx=K the the value of int_(4 pi-2)^(4 pi)(sin((x)/(2)))/(4 pi+2-x)dx equals