What is the integral from 0 to sqrt(3 of)arctan(x) ?

The integral from 0 to sqrt(3 of)arctan(x) is (pi-sqrt(3)ln(2))/(sqrt(3))

integral from 0 to sqrt(3 of)arctan(x)

\int_{0}^{3} arctan (x) d x

\frac{π - 3 ln ( 2 )}{3}

Decimal

1.12065 \dots

Solution steps

\int_{0}^{3} arctan (x) d x

Apply Integration By Parts

= [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{0}^{3}

\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]_{0}^{3}

Simplify

[x arctan (x) - \frac{1}{2} ln x^{2} + 1]_{0}^{3} : [\frac{1}{2} (2 x arctan (x) - ln x^{2} + 1)]_{0}^{3}

= [\frac{1}{2} (2 x arctan (x) - ln x^{2} + 1)]_{0}^{3}

Compute the boundaries:

\frac{π - 3 ln ( 2 )}{3}

= \frac{π - 3 ln ( 2 )}{3}

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

d er i v a t i v e f (x) = \frac{x ^{2}}{7 + x}

x y^{^{'}} - 2 y = 2 y x^{2}

x \to 0 lim (x \cdot cot (2 x))

s l o p e y = x^{2} - 2 x - 3, (2, - 3)

What is the integral from 0 to sqrt(3 of)arctan(x) ?
The integral from 0 to sqrt(3 of)arctan(x) is (pi-sqrt(3)ln(2))/(sqrt(3))