What is the integral of arccot(10x) ?

The integral of arccot(10x) is xarccot(10x)+1/20 ln|100x^2+1|+C

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integral of arccot(10x)

\int arccot (10 x) d x

x arccot (10 x) + \frac{1}{20} ln 100 x^{2} + 1 + C

Solution steps

\int arccot (10 x) d x

Apply Integration By Parts

: x arccot (10 x) - \int - \frac{10 x}{100 x ^{2} + 1} d x

= x arccot (10 x) - \int - \frac{10 x}{100 x ^{2} + 1} d x

\int - \frac{10 x}{100 x ^{2} + 1} d x = - \frac{1}{20} ln 100 x^{2} + 1

= x arccot (10 x) - (- \frac{1}{20} ln 100 x^{2} + 1)

Simplify

= x arccot (10 x) + \frac{1}{20} ln 100 x^{2} + 1

Add a constant to the solution

= x arccot (10 x) + \frac{1}{20} ln 100 x^{2} + 1 + C

\frac{\partial}{\partial y} (e^{(x + y)})

\int \frac{x}{2 x + 7} d x

\frac{\partial}{\partial x} (5 cos (7 x - 3 y))

x \to 2 + lim (\frac{1}{∣ 2 - x ∣})

f (x) = (3 x^{6} + 8 x^{3})^{4}

What is the integral of arccot(10x) ?
The integral of arccot(10x) is xarccot(10x)+1/20 ln|100x^2+1|+C