`T h ev a l u eofint_1^((1+sqrt(5))/2)(x^2+1)/(x^4-x^2+1)log(1+x-1/x)dxi s` (a)`pi/8(log)_e2` (b) `pi/2(log)_e2` (c)`-pi/2(log)_e2` (d) none of these

T h ev a l u eofint_(-2)^2|1-x^2|dxi s_______

T h ev a l u eofint_0^1(2x^2+3x+3)/((x+1)(x^2+2x+2))dxi s pi/4+2log2-tan^(-1)2 pi/4+2log2-tan^(-1)1/3 2log2-cot^(-1)3 (d) -pi/4+log4+cot^(-1)2

int_0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logxdx is equal to (a) -pi/2lnpi (b) 0 (c) pi/2ln2 (d) none of these

The differential coefficient of f((log)_e x) with respect to x , where f(x)=(log)_e x , is (a) x/((log)_e x) (b) 1/x(log)_e x (c) 1/(x(log)_e x) (d) none of these

Evaluate int(1+x^(2)log_(e)x)/(x+x^(2)log_(e)x)dx

Evaluate int(log_(e)(x+sqrt(x^(2)+1)))/(sqrt(x^(2)+1))dx.

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

(log)_(x-1)x (log)_(x-2)(x-1) (log)_(x-12)(x-11)=2,x is equal to: 9 (b) 16 (c) 25 (d) none of these

If y=(log)_(sinx)(tanx),t h e n(((dy)/(dx)))_(pi/4)"is equal to" (a) 4/(log2) (b) -4log2 (c) (-4)/(log2) (d) none of these

If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y) is 1 (b) (log)_2 3-(log)_3 2 log(3/2) (d) none of these