What is the integral of (sec^2(θ))/(tan(θ)) ?

The integral of (sec^2(θ))/(tan(θ)) is ln|tan(θ)|+C

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integral of (sec^2(θ))/(tan(θ))

\int \frac{sec ^{2} ( θ )}{tan ( θ )} d θ

ln ∣ tan (θ) ∣ + C

Solution steps

\int \frac{sec ^{2} ( θ )}{tan ( θ )} d θ

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = tan (θ)

= ln ∣ tan (θ) ∣

Add a constant to the solution

= ln ∣ tan (θ) ∣ + C

x^{^{''}} - 2 x^{^{'}} - 3 x = 0

\frac{d}{d x} (2 x y)

x^{^{'}} = 6 (x^{2} + 1)

\frac{d}{d x} (1 0^{x^{2}})

\int_{0}^{4} \frac{1}{9 + x ^{2}} d x

What is the integral of (sec^2(θ))/(tan(θ)) ?
The integral of (sec^2(θ))/(tan(θ)) is ln|tan(θ)|+C