What is the integral of arccotan(x) ?

The integral of arccotan(x) is -ac^2roln|cos(x)|+C

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integral of arccotan(x)

\int a rcco tan (x) d x

- a c^{2} ro ln ∣ cos (x) ∣ + C

Solution steps

\int a rcco tan (x) d x

Take the constant out:

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

= a ccro \cdot \int tan (x) d x

Simplify

a ccro : a c^{2} ro

= a c^{2} ro \cdot \int tan (x) d x

Rewrite using trig identities

= a c^{2} ro \cdot \int \frac{sin ( x )}{cos ( x )} d x

Apply u-substitution

= a c^{2} ro \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

= a c^{2} ro (- \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= a c^{2} ro (- ln ∣ u ∣)

Substitute back

u = cos (x)

= a c^{2} ro (- ln ∣ cos (x) ∣)

Simplify

= - a c^{2} ro ln ∣ cos (x) ∣

Add a constant to the solution

= - a c^{2} ro ln ∣ cos (x) ∣ + C

\frac{d}{d x} (6 x^{3} x csc (x))

a re a x^{2}, x + 2, - 1, 2

\int sin^{5} (2 t) cos (2 t) d t

a re a 3 x^{3} - 2 x, - 3, 3

\frac{\partial}{\partial y} (\frac{1}{t ( y ^{2} - 9 )})

What is the integral of arccotan(x) ?
The integral of arccotan(x) is -ac^2roln|cos(x)|+C