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

The integral from 0 to 2 of arctan(x/2) is pi/2-ln(2)

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integral from 0 to 2 of arctan(x/2)

\int_{0}^{2} arctan (\frac{x}{2}) d x

\frac{π}{2} - ln (2)

Decimal Notation

0.87764 \dots

Solution steps

\int_{0}^{2} arctan (\frac{x}{2}) d x

Apply Integration By Parts

: [x arctan (\frac{x}{2}) - \int \frac{2 x}{x ^{2} + 4} d x]_{0}^{2}

= [x arctan (\frac{x}{2}) - \int \frac{2 x}{x ^{2} + 4} d x]_{0}^{2}

\int \frac{2 x}{x ^{2} + 4} d x = ln x^{2} + 4

= [x arctan (\frac{x}{2}) - ln x^{2} + 4]_{0}^{2}

Compute the boundaries:

\frac{π}{2} - ln (2)

= \frac{π}{2} - ln (2)

\frac{d}{d x} (- 0.0006 x (x - 15)^{2} (x - 40))

y = x (7 x + 3)^{\frac{1}{3}}

x \to 0 + lim (3 x^{x})

x \to + 0 lim (x^{3} cos (\frac{π}{x}))

\frac{\partial}{\partial x} (sin (2 x y))

What is the integral from 0 to 2 of arctan(x/2) ?
The integral from 0 to 2 of arctan(x/2) is pi/2-ln(2)