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

The integral of ((3+ln(2x))^3)/x is ((3+ln(2x))^4)/4+C

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integral of ((3+ln(2x))^3)/x

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

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

Solution steps

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

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = 3 + ln (2 x)

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

Add a constant to the solution

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

\frac{d v}{d t} = 9.8 - v

f (x) = x e^{2 x^{2} - 4 x}

y^{^{''}} + 4 y^{^{'}} + 5 y = - 15 x + 5 e^{- x}

\frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 2 x

\frac{d}{d x} (e^{3 x} - 1)

What is the integral of ((3+ln(2x))^3)/x ?
The integral of ((3+ln(2x))^3)/x is ((3+ln(2x))^4)/4+C