What is the integral of 9θsec^2(θ) ?

The integral of 9θsec^2(θ) is 9(θtan(θ)+ln|cos(θ)|)+C

Popular >

integral of 9θsec^2(θ)

\int 9 θ sec^{2} (θ) d θ

9 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

Solution steps

\int 9 θ sec^{2} (θ) d θ

Take the constant out:

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

= 9 \cdot \int θ sec^{2} (θ) d θ

Apply Integration By Parts

: θ tan (θ) - \int tan (θ) d θ

= 9 (θ tan (θ) - \int tan (θ) d θ)

\int tan (θ) d θ = - ln ∣ cos (θ) ∣

= 9 (θ tan (θ) - (- ln ∣ cos (θ) ∣))

Simplify

= 9 (θ tan (θ) + ln ∣ cos (θ) ∣)

Add a constant to the solution

= 9 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

\int sin (x) e^{2 c o s (x)} d x

\int 5 e^{x} - 7 sin (x) d x

\int (sin (x))^{'} d x

\int \frac{4 x ^{2} - 5 x - 15}{x ^{3} - 4 x ^{2} - 5 x} d x

\int e^{3 t a n (x)} sec^{2} (x) d x

What is the integral of 9θsec^2(θ) ?
The integral of 9θsec^2(θ) is 9(θtan(θ)+ln|cos(θ)|)+C