What is the integral of θsec^2(θ) ?

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

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integral of θsec^2(θ)

\int θ sec^{2} (θ) d θ

θ tan (θ) + ln ∣ cos (θ) ∣ + C

Solution steps

\int θ sec^{2} (θ) d θ

Apply Integration By Parts

: θ tan (θ) - \int tan (θ) d θ

= θ tan (θ) - \int tan (θ) d θ

\int tan (θ) d θ = - ln ∣ cos (θ) ∣

= θ tan (θ) - (- ln ∣ cos (θ) ∣)

Simplify

= θ tan (θ) + ln ∣ cos (θ) ∣

Add a constant to the solution

= θ tan (θ) + ln ∣ cos (θ) ∣ + C

sin (x^{4})

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