What is the integral from pi/4 to pi of cot(x) ?

The integral from pi/4 to pi of cot(x) is diverges

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integral from pi/4 to pi of cot(x)

\int_{\frac{π}{4}}^{π} cot (x) d x

diverges

Solution steps

\int_{\frac{π}{4}}^{π} cot (x) d x

Rewrite using trig identities

= \int_{\frac{π}{4}}^{π} \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

: \int_{\frac{2}{2}}^{0} \frac{1}{u} d u

= \int_{\frac{2}{2}}^{0} \frac{1}{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{\frac{2}{2}} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - [ln ∣ u ∣]_{0}^{\frac{2}{2}}

\frac{2}{2} = \frac{1}{2}

= - [ln ∣ u ∣]_{0}^{\frac{1}{2}}

Compute the boundaries:

diverges

= diverges

\int_{0}^{1} π (x - x^{2})^{2} d x

\int_{0}^{\infty} e^{x} sin (x) d x

\int_{0}^{4} 4 x^{3} d x

\int_{0}^{\frac{π}{4}} cos^{3} (2 x) d x

\int_{a}^{b} \frac{x}{b - a} d x

What is the integral from pi/4 to pi of cot(x) ?
The integral from pi/4 to pi of cot(x) is diverges