The value of definite integral `int_oo^0(z e^(-z))/(sqrt(1-e^(-2z)))dz`is equal to

The value of definite integral int_(oo)^(0)(ze^(-z))/(sqrt(1-e^(-2z)))dz is equal to

The value of the definite integral,int_(1)^(oo)(e^(x+1)+e^(3-x))^(-1)dx is

inte^zsqrt(4-e^(2z))dz

If the value of the definite integral int_(0)^(1)((e-1)sqrt(ln(1+(e-1)x))+e^(x^(2)))dx is e^(lambda) then lambda is equal to

inte^(2z)sqrt(e^(4z)+6)dz

int(dz)/(z sqrt(z^(2)-1))

Evaluate the following definite integrals: int_(0)^(oo)e^(-x)dx

Let f(x)=int _( z )^(2) (dy)/(sqrt(1+ y ^(3))). The value of the integral int _(0)^(2) xf (x ) dx is equal to:

lim_(hto0)(1)/(h)int_(x)^(x+h)(dz)/(z+sqrt(z^(2)+1)) is equal to -