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)(8log(1+x))/(1+x^(2))dx is: (1)pi log2 (2) (pi)/(8)log2(3)(pi)/(2)log2(4)log2

The value of int_0^1(8log(1+x))/(1+x^2)dx is a. pilog2 b. \ pi/8log2 c. \ pi/2log2 d. log2

The value of int_-1^3 [tan^-1(x/(x^2+1))+tan^-1((x^2+1)/x)]dx= (A) pi/2 (B) 2pi (C) pi (D) pi/4

The value of int_0^(log5) (e^xsqrt(e^x-1))/(e^x+3)dx is (A) 3+2pi (B) 4-pi (C) 2+pi (D) none of these

The value of the integral int_0^2("log"(x^2+2))/((x+2)^2)dx is (sqrt(2))/3tan^(-1)(sqrt(2))+5/(12)log2-1/4log3 b. (sqrt(2))/3tan^(-1)(sqrt(2))-5/(12)log2-1/4log3 c. (sqrt(2))/3tan^(-1)(sqrt(2))+5/(12)log2+1/4log3 d. (sqrt(2))/3tan^(-1)(sqrt(2))-5/(12)log2+1/(12)log3

Thevalueof int_(1)^((1+sqrt(5))/(2))(x^(2)+1)/(x^(4)-x^(2)+1)log(1+x-(1)/(x))dxis (a) (pi)/(8)(log)_(e)2(b)(pi)/(2)(log)_(e)2(c)-(pi)/(2)(log)_(e)2(d) none of these

int_0^(pi/4) 2 tan^3 x dx=1-log 2

tan^(-1)((2x)/(1-x^2))+cot^(-1)((1-x^2)/(2x))=pi/3

int_0^(pi//4) 2 tan^3 x dx=1-log 2