What is the integral of 12θsec^2(θ) ?

The integral of 12θsec^2(θ) is 12(θtan(θ)+ln|cos(θ)|)+C

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integral of 12θsec^2(θ)

\int 12 θ sec^{2} (θ) d θ

12 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

Solution steps

\int 12 θ sec^{2} (θ) d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 12 \cdot \int θ sec^{2} (θ) d θ

Apply Integration By Parts

: θ tan (θ) - \int tan (θ) d θ

= 12 (θ tan (θ) - \int tan (θ) d θ)

\int tan (θ) d θ = - ln ∣ cos (θ) ∣

= 12 (θ tan (θ) - (- ln ∣ cos (θ) ∣))

Simplify

= 12 (θ tan (θ) + ln ∣ cos (θ) ∣)

Add a constant to the solution

= 12 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

x e^{- x}

\frac{d y}{d x} + 3 x^{2} y = 10 x^{2}

x y + y^{^{'}} = 4 x

x \to + 1 + lim (1 - cos (2 (x - 1)))

\frac{\partial}{\partial x} (\frac{x}{y ^{2}})

What is the integral of 12θsec^2(θ) ?
The integral of 12θsec^2(θ) is 12(θtan(θ)+ln|cos(θ)|)+C