Question

Evaluate the integral of z tan z² dz

Answer 1

$I= \int z(tanz^2) dz$

Let $z^2=t\Rightarrow 2zdz=dt\\$

$\Rightarrow zdz=\dfrac{dt}{2}$

Now, $I= \int tan(t)\times \dfrac{dt}{2}$

$\Rightarrow I=\dfrac{1}{2}\int tan(t)dt$

$\Rightarrow I= \dfrac{1}{2}\times ln|sec(t)|+C$

$\Rightarrow I= \dfrac{1}{2}$ $ln |sec(z^2)|+C$

$\int ztan(z^2)dz=\dfrac{ln|sec(z^2)|}{2}+C$