What is the integral of ((1+ln(x))^2)/x ?

The integral of ((1+ln(x))^2)/x is ((1+ln(x))^3)/3+C

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integral of ((1+ln(x))^2)/x

\int \frac{( 1 + ln ( x ) ) ^{2}}{x} d x

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

Solution steps

\int \frac{( 1 + ln ( x ) ) ^{2}}{x} d x

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

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

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

Substitute back

u = 1 + ln (x)

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

Add a constant to the solution

= \frac{( 1 + ln ( x ) ) ^{3}}{3} + C

(y) \to (0) lim (3 x + 7 x y - 6 y)

x \to 1 lim (\frac{x}{∣ x ∣ - 1})

0.1 y^{^{'}} - 0.1 y = 0

f (x) = sin (x^{2})

\int_{1}^{2} \frac{x ^{6} + 4 x ^{8}}{x ^{5}} d x

What is the integral of ((1+ln(x))^2)/x ?
The integral of ((1+ln(x))^2)/x is ((1+ln(x))^3)/3+C