If `I=int(dx)/(x^(3)(x^(8)+1)^(3//4))=(lambda(1+x^(8))^((1)/(4)))/(x^(2))+c` (where c is the constant of integration), then the value of `lambda` is equal to

If the integral I=int(dx)/(x^(10)+x)=lambda ln ((x^(9))/(1+x^(mu)))+C , (where, C is the constant of integration) then the value of (1)/(lambda)+mu is equal to

The integral I=int2^((2^(x)+x))dx=lambda. (2^(2^(x)))+C (where, C is the constant of integration). Then the value of sqrtlambda is equal to

"If" int(dx)/((x^(2)-2x+10)^(2))=A("tan"^(-1)((x-1)/(3))+(f(x))/(x^(2)-2x+10))+C ,where, C is a constant of integration, then

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

If int(dx)/(x^(3)(1+x^(6))^(2/3))=xf(x)(1+x^(6))^(1/3)+C where, C is a constant of integration, then the function f(x) is equal to

If int(dx)/((x^(2)+x+1)^(2))=atan^(-1)((2x+1)/(sqrt(3)))+b((2x+1)/(x^(2)+x+1))+C , x gt 0 where C is the constant of integration, then the value of 9(sqrt(3)a+b) is equal to __________.

If the integral I=inte^(x^(2))x^(3)dx=e^(x^(2))f(x)+c , where c is the constant of integration and f(1)=0 , then the value of f(2) is equal to

int(dx)/(1+e^(-x)) is equal to : Where c is the constant of integration.

If int x^(26).(x-1)^(17).(5x-3)dx=(x^(27).(x-1)^(18))/(k)+C where C is a constant of integration, then the value of k is equal to