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

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

Prove that int_0^(pi/2)(xdx)/(sinx)=int_0^1(sin^-1z)/(zsqrt(1-z^2))dz.

If x^(2)+y^(2)+z^(2)-2xyz=1 , then the value of (dx)/(sqrt(1-x^(2)))+(dy)/(sqrt(1-y^(2)))+(dz)/(sqrt(1-z^(2))) is equal to………..

If x^(2)+y^(2)+z^(2)-2xyz=1 , then the value of (dx)/(sqrt(1-x^(2)))+(dy)/(sqrt(1-y^(2)))+(dz)/(sqrt(1-z^(2))) is equal to………..

If x^(2)+y^(2)+z^(2)-2xyz=1 , then the value of (dx)/(sqrt(1-x^(2)))+(dy)/(sqrt(1-y^(2)))+(dz)/(sqrt(1-z^(2))) is equal to………..

If x^(2)+y^(2)+z^(2)-2xyz=1 , then the value of (dx)/(sqrt(1-x^(2)))+(dy)/(sqrt(1-y^(2)))+(dz)/(sqrt(1-z^(2))) is equal to………..

int_ (0) ^ ((pi) / (3)) (dz) / (sqrt (e ^ (z)))

If x=int_(0)^(t^(2))e^(sqrt(z)){(2tan sqrt(z)+1-tan^(2)sqrt(z))/(2sqrt(z)sec^(2)sqrt(z))}dz and y=int_(0)^(t^(2))e^(sqrt(z)){(1-tan^(2)sqrt(z)-2tan sqrt(z))/(2sqrt(z)sec^(2)sqrt(z))}dz : Then the inclination of the tangent to the curve at t=(pi)/(4) is :

If x=int_(0)^(t^(2))e^(sqrt(z)){(2tan sqrt(z)+1-tan^(2)sqrt(z))/(2sqrt(z)sec^(2)sqrt(z))}dz and x=int_(0)^(t^(2))e^(sqrt(z)){(1-tan^(2)sqrt(z)-2tan sqrt(z))/(2sqrt(z)sec^(2)sqrt(z))}dz : Then the inclination of the tangent to the curve at t=(pi)/(4) is :

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