What is the integral of (arctan(x))/(x^3) ?

The integral of (arctan(x))/(x^3) is -(arctan(x))/(2x^2)+1/2 (-1/x-arctan(x))+C

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integral of (arctan(x))/(x^3)

\int \frac{arctan ( x )}{x ^{3}} d x

- \frac{arctan ( x )}{2 x ^{2}} + \frac{1}{2} (- \frac{1}{x} - arctan (x)) + C

Solution steps

\int \frac{arctan ( x )}{x ^{3}} d x

Apply Integration By Parts

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

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

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

= - \frac{arctan ( x )}{2 x ^{2}} - (- \frac{1}{2} (- \frac{1}{x} - arctan (x)))

Simplify

= - \frac{arctan ( x )}{2 x ^{2}} + \frac{1}{2} (- \frac{1}{x} - arctan (x))

Add a constant to the solution

= - \frac{arctan ( x )}{2 x ^{2}} + \frac{1}{2} (- \frac{1}{x} - arctan (x)) + C

\int 14 x^{6} y^{- 4} - 12 x^{5 y^{- 3}} d x

\frac{\partial}{\partial x} (cos (2 x - y))

\int x ln (x^{6}) d x

\frac{d}{d x} (4 x^{2} y)

x = - 5, x = 3, y = 10 x, y = x^{2} - 11

What is the integral of (arctan(x))/(x^3) ?
The integral of (arctan(x))/(x^3) is -(arctan(x))/(2x^2)+1/2 (-1/x-arctan(x))+C