What is ln|x^2+9|-1/3 arctan(x/3)+3ln|x| ?

The solution to ln|x^2+9|-1/3 arctan(x/3)+3ln|x| is ln(|x^2+9||x|^3)-1/3 arctan(x/3)

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simplify ln|x^2+9|-1/3 arctan(x/3)+3ln|x|

simplify

ln x^{2} + 9 - \frac{1}{3} arctan (\frac{x}{3}) + 3 ln ∣ x ∣

ln (x^{2} + 9 ∣ x ∣^{3}) - \frac{1}{3} arctan (\frac{x}{3})

Solution steps

ln x^{2} + 9 - \frac{1}{3} arctan (\frac{x}{3}) + 3 ln ∣ x ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln ∣ x ∣ = ln (∣ x ∣^{3})

= ln x^{2} + 9 - \frac{1}{3} arctan (\frac{x}{3}) + ln (∣ x ∣^{3})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln x^{2} + 9 + ln (∣ x ∣^{3}) = ln (∣ x ∣^{3} x^{2} + 9)

= ln (x^{2} + 9 ∣ x ∣^{3}) - \frac{1}{3} arctan (\frac{x}{3})

ln (\frac{11}{7})

ln (\frac{3}{2}) + ln (1)

- ln (x c)

ln (\frac{23.793}{29.759})

- 329 \cdot ln (\frac{1}{4})

What is ln|x^2+9|-1/3 arctan(x/3)+3ln|x| ?
The solution to ln|x^2+9|-1/3 arctan(x/3)+3ln|x| is ln(|x^2+9||x|^3)-1/3 arctan(x/3)