What is the integral of ztan^2(z) ?

The integral of ztan^2(z) is -z^2+ztan(z)+(z^2)/2+ln|cos(z)|+C

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integral of ztan^2(z)

\int z tan^{2} (z) d z

- z^{2} + z tan (z) + \frac{z ^{2}}{2} + ln ∣ cos (z) ∣ + C

Solution steps

\int z tan^{2} (z) d z

Apply Integration By Parts

: z (- z + tan (z)) - \int - z + tan (z) d z

= z (- z + tan (z)) - \int - z + tan (z) d z

\int - z + tan (z) d z = - \frac{z ^{2}}{2} - ln ∣ cos (z) ∣

= z (- z + tan (z)) - (- \frac{z ^{2}}{2} - ln ∣ cos (z) ∣)

Simplify

z (- z + tan (z)) - (- \frac{z ^{2}}{2} - ln ∣ cos (z) ∣) : - z^{2} + z tan (z) + \frac{z ^{2}}{2} + ln ∣ cos (z) ∣

= - z^{2} + z tan (z) + \frac{z ^{2}}{2} + ln ∣ cos (z) ∣

Add a constant to the solution

= - z^{2} + z tan (z) + \frac{z ^{2}}{2} + ln ∣ cos (z) ∣ + C

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What is the integral of ztan^2(z) ?
The integral of ztan^2(z) is -z^2+ztan(z)+(z^2)/2+ln|cos(z)|+C