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

f (x) = 6 x

\int_{0}^{1} 39 \frac{1}{x ^{p}} d x

ln (1 - x)

\int_{- 5}^{0} (2 + 25 - x^{2}) d x

x^{2} y^{^{'}} + (2 x^{2} - x) y = x^{4}

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