What is the integral from 0 to pi/4 of cot(x) ?

The integral from 0 to pi/4 of cot(x) is diverges

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integral from 0 to pi/4 of cot(x)

\int_{0}^{\frac{π}{4}} cot (x) d x

diverges

Solution steps

\int_{0}^{\frac{π}{4}} cot (x) d x

Rewrite using trig identities

= \int_{0}^{\frac{π}{4}} \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

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

= \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

f (x) = 5 x - 4 x^{2}, (- 1, - 9)

n = 0 \sum \infty \frac{5}{2 + 3 ^{n}}

\int \frac{csc ( x ) cot ( x )}{2 - csc ( x )} d x

\int e^{- x} (9 + e^{- x}) d x

y \to 6 lim (\frac{2 y ^{2} - 15 y + 18}{3 y ^{2} - 17 y - 6})

What is the integral from 0 to pi/4 of cot(x) ?
The integral from 0 to pi/4 of cot(x) is diverges