What is the integral of arccot(15x) ?

The integral of arccot(15x) is xarccot(15x)+1/30 ln|225x^2+1|+C

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integral of arccot(15x)

\int arccot (15 x) d x

x arccot (15 x) + \frac{1}{30} ln 225 x^{2} + 1 + C

Solution steps

\int arccot (15 x) d x

Apply Integration By Parts

: x arccot (15 x) - \int - \frac{15 x}{225 x ^{2} + 1} d x

= x arccot (15 x) - \int - \frac{15 x}{225 x ^{2} + 1} d x

\int - \frac{15 x}{225 x ^{2} + 1} d x = - \frac{1}{30} ln 225 x^{2} + 1

= x arccot (15 x) - (- \frac{1}{30} ln 225 x^{2} + 1)

Simplify

= x arccot (15 x) + \frac{1}{30} ln 225 x^{2} + 1

Add a constant to the solution

= x arccot (15 x) + \frac{1}{30} ln 225 x^{2} + 1 + C

\int 3 x + x^{2} y d x

\frac{1}{10} (e^{5 x} + e^{- 5 x})

y = e^{2 x} + x

f (x) = \frac{4 x}{x + 1}

\int \frac{x ^{5}}{( 8 - x ^{6} ) ^{2}} d x

What is the integral of arccot(15x) ?
The integral of arccot(15x) is xarccot(15x)+1/30 ln|225x^2+1|+C