What is the integral of (sec^2(x))/(1-tan(x)) ?

The integral of (sec^2(x))/(1-tan(x)) is -ln|1-tan(x)|+C

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integral of (sec^2(x))/(1-tan(x))

\int \frac{sec ^{2} ( x )}{1 - tan ( x )} d x

- ln ∣ 1 - tan (x) ∣ + C

Solution steps

\int \frac{sec ^{2} ( x )}{1 - tan ( x )} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = 1 - tan (x)

= - ln ∣ 1 - tan (x) ∣

Add a constant to the solution

= - ln ∣ 1 - tan (x) ∣ + C

\frac{d}{d x} (x^{3} + 3 x^{2} - 24)

x \to 2 lim (\frac{∣ x - 2 ∣}{x} + 6)

\int_{0}^{1} 2 π x (21 - 21 x) d x

(t - 1) cos (4 t - 4)

\frac{\partial}{\partial x} (e^{- t} \cdot cos (π x))

What is the integral of (sec^2(x))/(1-tan(x)) ?
The integral of (sec^2(x))/(1-tan(x)) is -ln|1-tan(x)|+C