What is the integral of (ln^2(x))/(x^{5/3)} ?

The integral of (ln^2(x))/(x^{5/3)} is -(3ln^2(x))/(2x^{2/3)}+3(-(3ln(x))/(2x^{2/3)}-9/(4x^{2/3)})+C

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integral of (ln^2(x))/(x^{5/3)}

\int \frac{ln ^{2} ( x )}{x ^{\frac{5}{3}}} d x

- \frac{3 ln ^{2} ( x )}{2 x ^{\frac{2}{3}}} + 3 (- \frac{3 ln ( x )}{2 x ^{\frac{2}{3}}} - \frac{9}{4 x ^{\frac{2}{3}}}) + C

Solution steps

\int \frac{ln ^{2} ( x )}{x ^{\frac{5}{3}}} d x

Apply Integration By Parts

: - \frac{3 ln ^{2} ( x )}{2 x ^{\frac{2}{3}}} - \int - \frac{3 ln ( x )}{x ^{\frac{5}{3}}} d x

= - \frac{3 ln ^{2} ( x )}{2 x ^{\frac{2}{3}}} - \int - \frac{3 ln ( x )}{x ^{\frac{5}{3}}} d x

\int - \frac{3 ln ( x )}{x ^{\frac{5}{3}}} d x = - 3 (- \frac{3 ln ( x )}{2 x ^{\frac{2}{3}}} - \frac{9}{4 x ^{\frac{2}{3}}})

= - \frac{3 ln ^{2} ( x )}{2 x ^{\frac{2}{3}}} - (- 3 (- \frac{3 ln ( x )}{2 x ^{\frac{2}{3}}} - \frac{9}{4 x ^{\frac{2}{3}}}))

Simplify

= - \frac{3 ln ^{2} ( x )}{2 x ^{\frac{2}{3}}} + 3 (- \frac{3 ln ( x )}{2 x ^{\frac{2}{3}}} - \frac{9}{4 x ^{\frac{2}{3}}})

Add a constant to the solution

= - \frac{3 ln ^{2} ( x )}{2 x ^{\frac{2}{3}}} + 3 (- \frac{3 ln ( x )}{2 x ^{\frac{2}{3}}} - \frac{9}{4 x ^{\frac{2}{3}}}) + C

x \to \infty lim (∣ 1 ∣)

\int_{0}^{t} e^{u} d u

x \to \infty lim (4^{x})

\int_{- 1}^{2} (7 - 3 x) d x

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

What is the integral of (ln^2(x))/(x^{5/3)} ?
The integral of (ln^2(x))/(x^{5/3)} is -(3ln^2(x))/(2x^{2/3)}+3(-(3ln(x))/(2x^{2/3)}-9/(4x^{2/3)})+C