What is the integral of 19θsec^2(θ) ?

The integral of 19θsec^2(θ) is 19(θtan(θ)+ln|cos(θ)|)+C

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integral of 19θsec^2(θ)

\int 19 θ sec^{2} (θ) d θ

19 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

Solution steps

\int 19 θ sec^{2} (θ) d θ

Take the constant out:

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

= 19 \cdot \int θ sec^{2} (θ) d θ

Apply Integration By Parts

: θ tan (θ) - \int tan (θ) d θ

= 19 (θ tan (θ) - \int tan (θ) d θ)

\int tan (θ) d θ = - ln ∣ cos (θ) ∣

= 19 (θ tan (θ) - (- ln ∣ cos (θ) ∣))

Simplify

= 19 (θ tan (θ) + ln ∣ cos (θ) ∣)

Add a constant to the solution

= 19 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

x \to 0 + lim (tan^{x^{2}} (x))

tan (6 x)

\frac{1}{x + 3}

x \to 0 lim (\frac{sin ( 7 x )}{tan ( x )})

\int \frac{2 x ^{2} + x - 8}{x ^{3} - 4 x} d x

What is the integral of 19θsec^2(θ) ?
The integral of 19θsec^2(θ) is 19(θtan(θ)+ln|cos(θ)|)+C