`int_0^3(3x+1)/(x^2+9)dx` = `(pi^)/(12)+log(2sqrt(2))` (b) `(pi^)/2+log(2sqrt(2))` (c) `(pi^)/6+log(2sqrt(2))` (d) `(pi^)/3+log(2sqrt(2))`

int_0^(4/pi) (3x^2sin(1/x)-xcos(1/x))dx= (A) (8sqrt(2))/pi^3 (B) (32sqrt(2))/pi^3 (C) (24sqrt(2))/pi^3 (D) sqrt(2048)/pi^3

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

If int_0^(pi/3)(cosx)/(3+4sinx) dx=k log((3+2sqrt(3))/3), then k is equal to

The value of int_(-1)^(1) (log(x+sqrt(1+x^(2))))/(x+log(x+sqrt(1+x^(2))))f(x) dx-int_(-1)^(1) (log(x +sqrt(1+x^(2))))/(x+log(x+sqrt(1+x^(2))))f(-x)dx ,

Prove that pi/6 lt int_0^1(dx) (sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))

The value of the definite integral int_0^(pi/2)sqrt(tanx)dx is sqrt(2)pi (b) pi/(sqrt(2)) 2sqrt(2)pi (d) pi/(2sqrt(2))

Compute the following 56+(log)_(sqrt(2))4/(sqrt(7)+sqrt(3))+(log)_(1//2)1/(10+2sqrt(21))

Prove that pi/6

Prove that : int_(0)^(1) (log x)/(sqrt(1-x^(2)))dx=-(pi)/(2)log 2

Statement-1: int_(0)^(pi//2) x cot x dx=(pi)/(2)log2 Statement-2: int_(0)^(pi//2) log sin x dx=-(pi)/(2)log2