What is the integral of (arctan(x))/(x^2) ?

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

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integral of (arctan(x))/(x^2)

\int \frac{arctan ( x )}{x ^{2}} d x

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

Solution steps

\int \frac{arctan ( x )}{x ^{2}} d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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

\int \frac{x}{x ^{2} + 36} d x

\frac{\partial}{\partial x} ((3 + x^{2} - 3 y^{2})^{\frac{1}{2}})

2 x (\frac{d y}{d x}) - 10 y = x^{- 6}

x^{2} e^{3 x}

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