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

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

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

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

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

Decimal Notation

0.68182 \dots

Solution steps

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

Apply Integration By Parts

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

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

Simplify

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

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

Compute the boundaries:

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

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

\int_{- \infty}^{2} (x - 2) e^{x} d x

\int_{- 1}^{1} e^{x} - x^{2} + 2 d x

\int_{- 1}^{1} cos (x^{2}) d x

\int_{0}^{π} (3 x^{2} y - 4 sin (y)) d y

\int_{- 2}^{- 1} (x^{- 4}) d x

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