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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

d er i v a t i v e f (x) = x^{2} - 4 x + 3

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

\int sin (x) \cdot sin (3 x) d x

\int 2 cos^{2} (2 x) d x

d er i v a t i v e s (t) = 4 e^{- 2 t} sin (2 π t)

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