The value of `int_0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dxi s`

The value of int_0^1(x^4(1-x)^4)/(1+x^2)\ dx is

The value of int_(0)^(1)xcos^(-1)((1-x^2)/(1+x^2)) dx (x>0) is equal to ___________.

The value of int_1^e((tan^(-1)x)/x+(logx)/(1+x^2))dxi s tane (b) tan^(-1)e tan^(-1)(1/e) (d) none of these

The value of int_0^1(2x^2+3x+3)/((x+1)(x^2+2x+2))dx is (a) pi/4+2log2-tan^(-1)2 (b) pi/4+2log2-tan^(-1)1/3 (c) 2log2-cot^(-1)3 (d) -pi/4+log4+cot^(-1)2

The value of int_0^1(x^4(1-x)^4)/(1+x^2)dx is/are (a) (22)/7-pi (b) 2/(105) (c) 0 (d) (71)/(15)-(3pi)/2

The value of int_(0)^(1)tan^(-1)((2x-1)/(1+x-x^(2)))dx 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 .