What is the integral from 0 to pi/2 of cot(x) ?

The integral from 0 to pi/2 of cot(x) is diverges

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integral from 0 to pi/2 of cot(x)

\int_{0}^{\frac{π}{2}} cot (x) d x

diverges

Solution steps

\int_{0}^{\frac{π}{2}} cot (x) d x

Rewrite using trig identities

= \int_{0}^{\frac{π}{2}} \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{0}^{1}

Compute the boundaries:

diverges

= diverges

x \to 0 lim ((1 + 8 x)^{\frac{6}{x}})

\frac{4 - 3 x - x ^{2}}{x ^{2} - 1}

\frac{d x}{d y} = 3 x

\int_{\frac{1}{2}}^{3} \frac{1}{x ^{2}} d x

\int_{0}^{2 π} (x^{2} sin (2 x)) d x

What is the integral from 0 to pi/2 of cot(x) ?
The integral from 0 to pi/2 of cot(x) is diverges