If `int_0^oox^(2n+1)dote^(-x^2)dx=360 ,` then the value of `n` is___

If int_0^1e^-(x^2)dx=a , then find the value of int_0^1x^2e^-(x^2)dx in terms of a .

If intx^2dote^(-2x)dx=e^(-2x)(a x^2+b x+c)+d , then the value of |a/(b c)| is______

If f(x)=int(3x^2+1)/((x^2-1)^3)dxa n df(0)=0, then the value of |2/(f(2))| is___

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_2^(-1)f(x)dxdot

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

Prove that: I_n=int_0^oox^(2n+1)e^-x^2dx=(n !)/2,n in Ndot

Let I_(n)=int_(0)^(pi//2)(sinx+cosx)^(n)dx(nge2) . Then the value of n. I_(n)-2(n-1)I_(n-1) is

Evaluate int_(0)^(1)x(1-x)^(n)dx

If 2tan^2x-5secx=1 is satisfied by exactly seven distinct values of x in [0,((2n+1)pi)/2],n in N , then the greatest value of n is________.

If U_n=int_0^1x^n(2-x)^ndxa n dV_n=int_0^1x^n(1-x)^n dx ,n in N , and if (V_n)/(U_n)=1024 , then the value of n is________