What is the integral from-sqrt(3) to-1 of arctan(x) ?

The integral from-sqrt(3) to-1 of arctan(x) is 1/2 ln(2)+pi/4-pi/(sqrt(3))

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integral from-sqrt(3) to-1 of arctan(x)

\int_{- 3}^{- 1} arctan (x) d x

\frac{1}{2} ln (2) + \frac{π}{4} - \frac{π}{3}

Decimal

- 0.68182 \dots

Solution steps

\int_{- 3}^{- 1} arctan (x) d x

Apply Integration By Parts

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

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

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

Compute the boundaries:

\frac{1}{2} ln (2) + \frac{π}{4} - \frac{π}{3}

= \frac{1}{2} ln (2) + \frac{π}{4} - \frac{π}{3}

What is the integral from-sqrt(3) to-1 of arctan(x) ?
The integral from-sqrt(3) to-1 of arctan(x) is 1/2 ln(2)+pi/4-pi/(sqrt(3))