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

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

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

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

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

Solution steps

\int \frac{( 2 + ln ( 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 = 2 + ln (x)

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

Add a constant to the solution

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

cos^{2} (t)

\int \frac{1}{2}

\int sin (a x) e^{b x + c} d x

\int 5 sin (6 - 5 x) d x

\int \frac{9}{x - 7} d x

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