What is the integral of x^3arccot(x) ?

The integral of x^3arccot(x) is 1/4 x^4arccot(x)+1/4 ((x^3)/3-x+arctan(x))+C

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integral of x^3arccot(x)

\int x^{3} arccot (x) d x

\frac{1}{4} x^{4} arccot (x) + \frac{1}{4} (\frac{x ^{3}}{3} - x + arctan (x)) + C

Solution steps

\int x^{3} arccot (x) d x

Apply Integration By Parts

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

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

\int - \frac{x ^{4}}{4 ( x ^{2} + 1 )} d x = - \frac{1}{4} (\frac{x ^{3}}{3} - x + arctan (x))

= \frac{1}{4} x^{4} arccot (x) - (- \frac{1}{4} (\frac{x ^{3}}{3} - x + arctan (x)))

Simplify

= \frac{1}{4} x^{4} arccot (x) + \frac{1}{4} (\frac{x ^{3}}{3} - x + arctan (x))

Add a constant to the solution

= \frac{1}{4} x^{4} arccot (x) + \frac{1}{4} (\frac{x ^{3}}{3} - x + arctan (x)) + C

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What is the integral of x^3arccot(x) ?
The integral of x^3arccot(x) is 1/4 x^4arccot(x)+1/4 ((x^3)/3-x+arctan(x))+C