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))

integral

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

\frac{sin ^{2} ( x )}{cos ( x )}

\frac{( 2 + e ^{x} )}{e ^{x}}

(16 - x^{2})^{\frac{1}{2}}

\frac{a}{( a ^{2} + x ^{2} )}

\frac{x}{( 1 + x )}

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