What is the integral of ((1+ln(x))^3)/x ?

The integral of ((1+ln(x))^3)/x is ((1+ln(x))^4)/4+C

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integral of ((1+ln(x))^3)/x

\int \frac{( 1 + ln ( x ) ) ^{3}}{x} d x

\frac{( 1 + ln ( x ) ) ^{4}}{4} + C

Solution steps

\int \frac{( 1 + 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 = 1 + ln (x)

= \frac{( 1 + ln ( x ) ) ^{4}}{4}

Add a constant to the solution

= \frac{( 1 + ln ( x ) ) ^{4}}{4} + C

\int (3 x + 1) (4 - x) d x

\frac{( x - 2 )}{x + 3}

\frac{d}{d x} (3 x y)

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

\frac{d}{d x} (ln (arctan (8 x^{5})))

What is the integral of ((1+ln(x))^3)/x ?
The integral of ((1+ln(x))^3)/x is ((1+ln(x))^4)/4+C