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

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

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

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

ln tan (\frac{x}{2}) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{1}{sin ( 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 (\frac{x}{2})

= ln tan (\frac{x}{2})

Add a constant to the solution

= ln tan (\frac{x}{2}) + C

(1 + x) y^{^{'}} = y + x

y = 3 arctan (x + 1 + x^{2})

\int (e^{2 x} sin (3 x)) d x

x (x - 1)^{2}

\int 3 x sin (2 x) d x

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