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

1 + 2 x

\int \frac{1}{t ^{2} - 1} d t

\frac{d}{d x} (x^{2} + \frac{y ^{2}}{9}) = 1

t^{\frac{3}{2}}

y = \frac{3}{2} x, y = 7 - x^{2}

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