What is the integral from 0 to 1 of arctan(2x) ?

The integral from 0 to 1 of arctan(2x) is arctan(2)-1/4 ln(5)

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integral from 0 to 1 of arctan(2x)

\int_{0}^{1} arctan (2 x) d x

arctan (2) - \frac{1}{4} ln (5)

Decimal Notation

0.70478 \dots

Solution steps

\int_{0}^{1} arctan (2 x) d x

Apply Integration By Parts

: [x arctan (2 x) - \int \frac{2 x}{4 x ^{2} + 1} d x]_{0}^{1}

= [x arctan (2 x) - \int \frac{2 x}{4 x ^{2} + 1} d x]_{0}^{1}

\int \frac{2 x}{4 x ^{2} + 1} d x = \frac{1}{4} ln 4 x^{2} + 1

= [x arctan (2 x) - \frac{1}{4} ln 4 x^{2} + 1]_{0}^{1}

Compute the boundaries:

arctan (2) - \frac{1}{4} ln (5)

= arctan (2) - \frac{1}{4} ln (5)

\int x (x - 5)^{2} d x

\frac{d}{d x} (\frac{3}{6 x ^{- 2}})

f (x) = \frac{x ^{3}}{24} + \frac{2}{x}

\int_{1}^{2} \frac{1}{4 - t ^{2}} d t

- 3 x^{2} + 2 x y + 2 y^{3} = 125, (3, 4)

What is the integral from 0 to 1 of arctan(2x) ?
The integral from 0 to 1 of arctan(2x) is arctan(2)-1/4 ln(5)