What is the integral from 2 to 7 of 5arccot(x) ?

The integral from 2 to 7 of 5arccot(x) is 5(7arccot(7)-2arccot(2)+(ln(10))/2)

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integral from 2 to 7 of 5arccot(x)

\int_{2}^{7} 5 arccot (x) d x

5 (7 arccot (7) - 2 arccot (2) + \frac{ln ( 10 )}{2})

Decimal

6.08638 \dots

Solution steps

\int_{2}^{7} 5 arccot (x) d x

Take the constant out:

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

= 5 \cdot \int_{2}^{7} arccot (x) d x

Apply Integration By Parts

= 5 [x arccot (x) - \int - \frac{x}{x ^{2} + 1} d x]_{2}^{7}

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

= 5 [x arccot (x) - (- \frac{1}{2} ln x^{2} + 1)]_{2}^{7}

Simplify

= 5 [x arccot (x) + \frac{1}{2} ln x^{2} + 1]_{2}^{7}

Compute the boundaries:

7 arccot (7) - 2 arccot (2) + \frac{ln ( 50 ) - ln ( 5 )}{2}

= 5 (7 arccot (7) - 2 arccot (2) + \frac{ln ( 50 ) - ln ( 5 )}{2})

Simplify

= 5 (7 arccot (7) - 2 arccot (2) + \frac{ln ( 10 )}{2})

What is the integral from 2 to 7 of 5arccot(x) ?
The integral from 2 to 7 of 5arccot(x) is 5(7arccot(7)-2arccot(2)+(ln(10))/2)