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

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=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_(c^(2))^(tan t)tan^(-1)z dz, y= int_(n)^(sqrt(t))(cos(z^(2)))/(z)dx then (dy)/(dx) is equal to : (where c and n are constants) :

Solve l=int_(cos^(4)t)^(-sin^(4)t)(sqrt(f(z))dz)/(sqrt(f(cos 2 t -z))+sqrt(f(z)))

If |z-(1/z)|=1, then a. (|z|)_(m a x)=(1+sqrt(5))/2 b. (|z|)_(m in)=(sqrt(5)-1)/2 c. (|z|)_(m a x)=(sqrt(5)-2)/2 d. (|z|)_(m in)=(sqrt(5)-1)/(sqrt(2))

If I_(1)=int_(0)^(x) e^("zx ")e^(-z^(2))dz and I_(2)=int_(0)^(x) e^(-z^(2)//4)dz , them

If y= (1)/( a-z) , show that (dz)/( dy) = (z-a)^(2)

If z_1, z_2a n dz_3, z_4 are two pairs of conjugate complex numbers, find the a rg((z1)/(z4))+a rg((z2)/(z3)) =0

For z_(1)=""^(6)sqrt((1-i)//(1+isqrt(3))),z_(2)=""^(6)sqrt((1-i)//(sqrt(3)+i)) , z_(3)= ""^(6)sqrt((1+i) //(sqrt(3)-i)) , prove that |z_(1)|=|z_(2)|=|z_(3)|

If log sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt2 , then the locus of z is