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

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

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integral of (sec^2(x))/(tan(x))

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

ln ∣ tan (x) ∣ + C

Solution steps

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

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 (x)

= ln ∣ tan (x) ∣

Add a constant to the solution

= ln ∣ tan (x) ∣ + C

f (x) = x^{2} - 4 x + 3

\frac{d}{d x} (\frac{x ^{2} sin ( x )}{e ^{x}})

\frac{\partial}{\partial x} (x^{2} y^{5})

- 5 x^{2} y + y^{^{'}} = 5 x^{2}

\int ((sec (x))^{2} - csc (x) cot (x)) d x

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