if` int (1+x^n)^(1/n)/x^(n+2)dx`=`a(1+1/x^4)^b+c` then value of `a+b=`

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

11. int_(1)^(2)dx/(x.(x^n+1))

If int_0^oo x^(2n+1)\ e^(-x^2)\ dx=360, then the value of n is___

Suppose for every integer n, .int_(n)^(n+1) f(x)dx = n^(2) . The value of int_(-2)^(4) f(x)dx is :

If mgt0, ngt0 , the definite integral I=int_0^1 x^(m-1)(1-x)^(n-1)dx depends upon the values of m and n is denoted by beta(m,n) , called the beta function.Obviously, beta(n,m)=beta(m,n) .Now answer the question:If int_0^oo x^(m-1)/(1+x)^(m+n)dx=k int_0^oo x^(n-1)/(1+x)^(m+n)dx , then k is equal to (A) m/n (B) 1 (C) n/m (D) none of these

If y=a[x+(x^2-1)^(1/2)]^n+b[x-(x^2-1)^(1/2)]^n the value of the expression (x^2-1)(d^2y) / dx^2+x dy / dx-n^2y is __________.

ifint(dx)/(x^2(x^n+1)^(((n-1)/n)) )=-[f(x)]^(1/n)+c ,t h e nf(x)i s (a) (1+x^n) (b) 1+x^(-1) (c) x^n+x^(-n) (d) none of these

If I_(n)=int_(0)^(1)(1+x+x^(2)+....+x^(n-1))(1+3x+5x^(2)+....+(2n-3)x^(n-2)+(2n-1)x^(n-1))dx,n in N, then the value of sqrt(I_(9)) is (a) 3 (b) 6 (c) 9 (d) 12

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________

Let I_(n) = int_(0)^(1)x^(n)(tan^(1)x)dx, n in N , then