What is the integral of 6/(xln^3(x)) ?

The integral of 6/(xln^3(x)) is -3/(ln^2(x))+C

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integral of 6/(xln^3(x))

\int \frac{6}{x ln ^{3} ( x )} d x

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

Solution steps

\int \frac{6}{x ln ^{3} ( x )} d x

Take the constant out:

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

= 6 \cdot \int \frac{1}{x ln ^{3} ( x )} d x

Apply u-substitution

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

= 6 \cdot \int \frac{1}{u ^{3}} d u

Apply the Power Rule

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

= 6 (- \frac{1}{2 u ^{2}})

Substitute back

u = ln (x)

= 6 (- \frac{1}{2 ln ^{2} ( x )})

Simplify

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

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (ln (x^{5} + y^{5}))

\int \frac{8 + 4 x}{1 + x ^{2}} d x

f^{^{'}} (x) = 3.52 x^{2} - 30.1 x + 81

\frac{10}{x}

\frac{d}{d x} (e^{x + 8})

What is the integral of 6/(xln^3(x)) ?
The integral of 6/(xln^3(x)) is -3/(ln^2(x))+C