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

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

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

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

- \frac{1}{2 ( 1 + ln ( x ) ) ^{2}} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= - \frac{1}{2 u ^{2}}

Substitute back

u = 1 + ln (x)

= - \frac{1}{2 ( 1 + ln ( x ) ) ^{2}}

Add a constant to the solution

= - \frac{1}{2 ( 1 + ln ( x ) ) ^{2}} + C

\frac{d r}{d θ} = \frac{r ^{2} + 2 r θ}{θ ^{2}}

x \to 0 lim (\frac{x}{sin ( 8 x )})

x \to 1 lim (e^{x - 1} + 1)

\frac{\partial}{\partial x} (x ln (z^{7} + x^{4}))

y = x^{2} - 4 x - 3, (3, - 6)

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