What is the integral of cotan(x) ?

The integral of cotan(x) is -coln|cos(x)|+C

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integral of cotan(x)

\int co tan (x) d x

- co ln ∣ cos (x) ∣ + C

Solution steps

\int co tan (x) d x

Take the constant out:

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

= co \cdot \int tan (x) d x

Rewrite using trig identities

= co \cdot \int \frac{sin ( x )}{cos ( x )} d x

Apply u-substitution

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

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

Take the constant out:

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

= co (- \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= co (- ln ∣ u ∣)

Substitute back

u = cos (x)

= co (- ln ∣ cos (x) ∣)

Simplify

= - co ln ∣ cos (x) ∣

Add a constant to the solution

= - co ln ∣ cos (x) ∣ + C

x \to \frac{π}{3} lim (x cos (x))

y^{^{'}} + 2 y = e^{2 x}

x \to 0 + lim (lo g_{3} (x))

\int (10 x^{4} - 2 sec^{2} (x)) d x

(1 + x)^{- 2}