If `int(x-1)/((x+x sqrt(x)+sqrt(x))+sqrt(sqrt(x)(x+1)))dx=4tan^(-1)(g(x))+c` where `c` is constant of integration, then `g^(2)(1)=`

int sqrt((1+sqrt(x))/(1-sqrt(x))dx

If int(dx)/(sqrt(e^(x)-1))=2tan^(-1)(f(x))+C , (where x gt0 and C is the constant of integration ) then the range of f(x) is

int((sqrt(x)+1)(x^2-sqrt(x)))/(xsqrt(x)+x+sqrt(x))dx

int_(0)^(1)(1)/(sqrt(1+x)-sqrt(x))dx

If int (x+1)/(sqrt(2x-1))dx = f(x)sqrt(2x-1)+C , where C is a constant of integration, then f(x) is equal to

int(x+3sqrt(x^(2))+6sqrt(x))/(x(1+3sqrt(x)))dx

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

If int x^(5)e^(-x^(2))dx = g(x)e^(-x^(2))+C , where C is a constant of integration, then g(-1) is equal to

If the integral I=int(x^(5))/(sqrt(1+x^(3)))dx =Ksqrt(x^(3)+1)(x^(3)-2)+C , (where, C is the constant of integration), then the value of 9K is equal to

If I=int(x^(3)-1)/(x^(5)+x^(4)+x+1)dx=(1)/(4)ln(f(x))-ln(g(x))+c (where, c is the constant of integration) and f(0)=g(0)=1 ,then the value of f(1).g(1) is equal to