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

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

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

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

\frac{3}{5} (5 + ln (x))^{\frac{5}{3}} + C

Solution steps

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

Apply u-substitution

= \int u^{\frac{2}{3}} d u

Apply the Power Rule

= \frac{3}{5} u^{\frac{5}{3}}

Substitute back

u = 5 + ln (x)

= \frac{3}{5} (5 + ln (x))^{\frac{5}{3}}

Add a constant to the solution

= \frac{3}{5} (5 + ln (x))^{\frac{5}{3}} + C

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