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

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

Apply the Power Rule

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

= \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

\frac{\partial}{\partial y} (x^{5 y})

\int (x^{5}) d x

\int sin (x + \frac{π}{4}) d x

\int_{2}^{\infty} e^{- 3 p} d p

\int \frac{1}{e ^{π}} d x

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