Answer to Question #20341 in Calculus for sakura

Question

can you please help me this integral of [arccot sqrt(z)]/sqrt(z)?

Answer 1

From the definition, integral of arccotangent isz*arccot(z)+0.5ln(1+z^2)
To evaluate this integral we should change variables:t=sqrt(z)
So, dt=1/2sqrt(z)dz
Arccot(sqrt(z)/sqrt(z)dz=2arccot(t)dt
Integrating this we get:2*t*arccot(t)+ln(1+t^2)=2*sqrt(z)*arccot(sqrt(z))+ln(1+z)