What is the integral of arccot(5x) ?

The integral of arccot(5x) is xarccot(5x)+1/10 ln|25x^2+1|+C

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integral of arccot(5x)

\int arccot (5 x) d x

x arccot (5 x) + \frac{1}{10} ln 25 x^{2} + 1 + C

Solution steps

\int arccot (5 x) d x

Apply Integration By Parts

: x arccot (5 x) - \int - \frac{5 x}{25 x ^{2} + 1} d x

= x arccot (5 x) - \int - \frac{5 x}{25 x ^{2} + 1} d x

\int - \frac{5 x}{25 x ^{2} + 1} d x = - \frac{1}{10} ln 25 x^{2} + 1

= x arccot (5 x) - (- \frac{1}{10} ln 25 x^{2} + 1)

Simplify

= x arccot (5 x) + \frac{1}{10} ln 25 x^{2} + 1

Add a constant to the solution

= x arccot (5 x) + \frac{1}{10} ln 25 x^{2} + 1 + C

y^{^{'}} + \frac{2}{3} y = 1 - \frac{1}{2} t

\frac{d}{d x} (A (4 e^{2 x} x + 4 e^{2 x}))

\frac{d}{d x} ((x^{5} + 2 x) (x^{3} + x^{2} + x + 7))

\int \frac{1}{( x + 3 ) ^{2}} d x

y = 9 x^{2} ln (x), y = 36 ln (x)

What is the integral of arccot(5x) ?
The integral of arccot(5x) is xarccot(5x)+1/10 ln|25x^2+1|+C