What is the integral of (15arctan(x))/(x^2) ?

The integral of (15arctan(x))/(x^2) is 15(-(arctan(x))/x+ln|x|-1/2 ln|x^2+1|)+C

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integral of (15arctan(x))/(x^2)

\int \frac{15 arctan ( x )}{x ^{2}} d x

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

Solution steps

\int \frac{15 arctan ( x )}{x ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 15 \cdot \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

= 15 (- \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

= 15 (- \frac{arctan ( x )}{x} - (- ln ∣ x ∣ + \frac{1}{2} ln x^{2} + 1))

Simplify

= 15 (- \frac{arctan ( x )}{x} + ln ∣ x ∣ - \frac{1}{2} ln x^{2} + 1)

Add a constant to the solution

= 15 (- \frac{arctan ( x )}{x} + ln ∣ x ∣ - \frac{1}{2} ln x^{2} + 1) + C

\int_{x^{2}}^{1} ln (2 t^{2} + 1) d t

n = 5 \sum \infty e^{3 - 2 n}

\int 3 t^{2} sin (2 t^{3} + 1) d t

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

n = 1 \sum \infty \frac{17 n !}{n ^{n}}

What is the integral of (15arctan(x))/(x^2) ?
The integral of (15arctan(x))/(x^2) is 15(-(arctan(x))/x+ln|x|-1/2 ln|x^2+1|)+C