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

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

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integral of (-3)/(x(ln(x))^3)

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 3 \cdot \int \frac{1}{x ( ln ( x ) ) ^{3}} d x

Apply u-substitution

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

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

Apply the Power Rule

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

= - 3 (- \frac{1}{2 u ^{2}})

Substitute back

u = ln (x)

= - 3 (- \frac{1}{2 ln ^{2} ( x )})

Simplify

- 3 (- \frac{1}{2 ln ^{2} ( x )}) : \frac{3}{2 ln ^{2} ( x )}

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

Add a constant to the solution

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

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

\int \frac{- x + 4}{x ^{2} - 2 x + 4} d x

\int 7^{2 x} d x

\int \frac{x ^{2}}{x - x ^{2}} d x

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