What is the integral of arccot(2x) ?

The integral of arccot(2x) is xarccot(2x)+1/4 ln|4x^2+1|+C

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integral of arccot(2x)

\int arccot (2 x) d x

x arccot (2 x) + \frac{1}{4} ln 4 x^{2} + 1 + C

Solution steps

\int arccot (2 x) d x

Apply Integration By Parts

: x arccot (2 x) - \int - \frac{2 x}{4 x ^{2} + 1} d x

= x arccot (2 x) - \int - \frac{2 x}{4 x ^{2} + 1} d x

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

= x arccot (2 x) - (- \frac{1}{4} ln 4 x^{2} + 1)

Simplify

= x arccot (2 x) + \frac{1}{4} ln 4 x^{2} + 1

Add a constant to the solution

= x arccot (2 x) + \frac{1}{4} ln 4 x^{2} + 1 + C

t \to 0 lim (\frac{( 2 e ^{t} - 2 )}{t})

e^{x} x

x \to 0 + lim (\frac{- 2 x ^{4} - 14 x}{x})

\int t sin (2 t) d t

x \to 0 + lim (x^{2} sin (\frac{1}{x}))

What is the integral of arccot(2x) ?
The integral of arccot(2x) is xarccot(2x)+1/4 ln|4x^2+1|+C