What is the integral from-3 to 3 of arccot(x) ?

The integral from-3 to 3 of arccot(x) is 3arccot(3)+3arccot(-3)

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integral from-3 to 3 of arccot(x)

\int_{- 3}^{3} arccot (x) d x

3 arccot (3) + 3 arccot (- 3)

Decimal

9.42477 \dots

Solution steps

\int_{- 3}^{3} arccot (x) d x

Apply Integration By Parts

: [x arccot (x) - \int - \frac{x}{x ^{2} + 1} d x]_{- 3}^{3}

= [x arccot (x) - \int - \frac{x}{x ^{2} + 1} d x]_{- 3}^{3}

\int - \frac{x}{x ^{2} + 1} d x = - \frac{1}{2} ln x^{2} + 1

= [x arccot (x) - (- \frac{1}{2} ln x^{2} + 1)]_{- 3}^{3}

Simplify

= [x arccot (x) + \frac{1}{2} ln x^{2} + 1]_{- 3}^{3}

Compute the boundaries:

3 arccot (3) + 3 arccot (- 3)

= 3 arccot (3) + 3 arccot (- 3)

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\int_{1}^{3} \frac{12 ( ln ( x ) ) ^{3}}{x} d x

\int_{1}^{5} \frac{1}{x - 4} d x

What is the integral from-3 to 3 of arccot(x) ?
The integral from-3 to 3 of arccot(x) is 3arccot(3)+3arccot(-3)