What is the integral of (cot(x))/(cos^2(x)) ?

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

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integral of (cot(x))/(cos^2(x))

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

ln ∣ tan (x) ∣ + C

Solution steps

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

Rewrite using trig identities

= \int \frac{sec ( x )}{sin ( x )} d x

Apply Trigonometric 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

\int (1 + cot (x))^{4} (csc (x))^{2} d x

\int \frac{3 x ^{2} + 9 x + 1}{x} d x

\int \frac{sec ^{2} ( z )}{3 + 5 tan ( z )} d z

\int \frac{cos ( x )}{4} d x

\int sin (x^{2} + x) d x

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