What is the integral of 18θsec^2(θ) ?

The integral of 18θsec^2(θ) is 18(θtan(θ)+ln|cos(θ)|)+C

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integral of 18θsec^2(θ)

\int 18 θ sec^{2} (θ) d θ

18 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

Solution steps

\int 18 θ sec^{2} (θ) d θ

Take the constant out:

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

= 18 \cdot \int θ sec^{2} (θ) d θ

Apply Integration By Parts

: θ tan (θ) - \int tan (θ) d θ

= 18 (θ tan (θ) - \int tan (θ) d θ)

\int tan (θ) d θ = - ln ∣ cos (θ) ∣

= 18 (θ tan (θ) - (- ln ∣ cos (θ) ∣))

Simplify

= 18 (θ tan (θ) + ln ∣ cos (θ) ∣)

Add a constant to the solution

= 18 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

\int ln^{3} (x) d x

\int \frac{sin ( t )}{cos ^{3} ( t )} d t

x \to - 3 lim (1)

\frac{d}{d x} (x^{3} \cdot cos (x))

\frac{d}{d x} (3 x^{\frac{2}{3}} - 6 x^{\frac{1}{3}} + x^{- \frac{1}{3}})

What is the integral of 18θsec^2(θ) ?
The integral of 18θsec^2(θ) is 18(θtan(θ)+ln|cos(θ)|)+C