What is the integral of (-8)/(x(ln(x))^2) ?

The integral of (-8)/(x(ln(x))^2) is 8/(ln(x))+C

Popular >

integral of (-8)/(x(ln(x))^2)

\int \frac{- 8}{x ( ln ( x ) ) ^{2}} d x

\frac{8}{ln ( x )} + C

Solution steps

\int \frac{- 8}{x ( ln ( x ) ) ^{2}} d x

Take the constant out:

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

= - 8 \cdot \int \frac{1}{x ( ln ( x ) ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= - 8 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - 8 (- \frac{1}{u})

Substitute back

u = ln (x)

= - 8 (- \frac{1}{ln ( x )})

Simplify

- 8 (- \frac{1}{ln ( x )}) : \frac{8}{ln ( x )}

= \frac{8}{ln ( x )}

Add a constant to the solution

= \frac{8}{ln ( x )} + C

\int 54 (1 + x^{2}) (7 + 18 x + 6 x^{3})^{10} d x

\int 9 tan (3 + 9 x) d x

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

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

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

What is the integral of (-8)/(x(ln(x))^2) ?
The integral of (-8)/(x(ln(x))^2) is 8/(ln(x))+C