What is the integral of θtan^2(θ) ?

The integral of θtan^2(θ) is -θ^2+θtan(θ)+(θ^2)/2+ln|cos(θ)|+C

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integral of θtan^2(θ)

\int θ tan^{2} (θ) d θ

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

Solution steps

\int θ tan^{2} (θ) d θ

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

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