What is the integral of 10θsec^2(θ) ?

The integral of 10θsec^2(θ) is 10(θtan(θ)+ln|cos(θ)|)+C

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integral of 10θsec^2(θ)

\int 10 θ sec^{2} (θ) d θ

10 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

Solution steps

\int 10 θ sec^{2} (θ) d θ

Take the constant out:

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

= 10 \cdot \int θ sec^{2} (θ) d θ

Apply Integration By Parts

: θ tan (θ) - \int tan (θ) d θ

= 10 (θ tan (θ) - \int tan (θ) d θ)

\int tan (θ) d θ = - ln ∣ cos (θ) ∣

= 10 (θ tan (θ) - (- ln ∣ cos (θ) ∣))

Simplify

= 10 (θ tan (θ) + ln ∣ cos (θ) ∣)

Add a constant to the solution

= 10 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

\int_{2}^{5} \frac{x}{x ^{2} - 4} d x

f (x) = \frac{- 1}{2 x} + 2 x

\frac{d}{d x} (cos (x^{- 4}))

x \to 2 lim (\frac{5}{x - 2})

(3, - 3), (5, - 6)

What is the integral of 10θsec^2(θ) ?
The integral of 10θsec^2(θ) is 10(θtan(θ)+ln|cos(θ)|)+C