What is the integral of 12θsec^2(θ) ?

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

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

= 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

d er i v a t i v e 4 x^{2} - 2 x (- 9)

\int \frac{2 x + 3}{x ^{2} - 9} d x

\frac{d}{d x} (x 25 - x^{2})

\int \frac{3 x - 4}{( x - 1 ) ( x + 2 )} d x

x^{^{''}} + 2 x^{^{'}} + 5 x = 0, x (0) = 1, x^{^{'}} (0) = - 1

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