What is the integral of 17θsec^2(θ) ?

The integral of 17θsec^2(θ) is 17(θtan(θ)+ln|cos(θ)|)+C

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integral of 17θsec^2(θ)

\int 17 θ sec^{2} (θ) d θ

17 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

Solution steps

\int 17 θ sec^{2} (θ) d θ

Take the constant out:

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

= 17 \cdot \int θ sec^{2} (θ) d θ

Apply Integration By Parts

: θ tan (θ) - \int tan (θ) d θ

= 17 (θ tan (θ) - \int tan (θ) d θ)

\int tan (θ) d θ = - ln ∣ cos (θ) ∣

= 17 (θ tan (θ) - (- ln ∣ cos (θ) ∣))

Simplify

= 17 (θ tan (θ) + ln ∣ cos (θ) ∣)

Add a constant to the solution

= 17 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

y = e^{c x}

\int_{0}^{4} (5 - x) x d x

x e^{y}

\int \frac{1}{x ^{2} + 4 x - 5} d x

t^{2} y^{^{'}} + 2 t y = y^{3}

What is the integral of 17θsec^2(θ) ?
The integral of 17θsec^2(θ) is 17(θtan(θ)+ln|cos(θ)|)+C