If `int(3z^3-8z+5)/(sqrt(z^2-4z-7))dz=(z^2+az+36)sqrt(z^2-4z-7)+bln|z-2+sqrt(z^2-4z-7)|+C` ,where `a,b in I and C` is integretion constant , then

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

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

Show that |(2z + 5)(sqrt2-i)|=sqrt(3) |2z+5| , where z is a complex number.

Show that |(2z + 5)(sqrt2-i)|=sqrt(3) |2z+5| , where z is a complex number.

(4+z-(3+2z))/(6) =(-z -3 (5-2))/(7) What is the value of z in the equation above ?

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 :

If z_(1)=sqrt(3)-i, z_(2)=1+i sqrt(3) , then amp (z_(1)+z_(2))=