What is the integral of 4/(x(ln(x))^2) ?

The integral of 4/(x(ln(x))^2) is -4/(ln(x))+C

Popular >

integral of 4/(x(ln(x))^2)

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

- \frac{4}{ln ( x )} + C

Solution steps

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

Take the constant out:

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

= 4 \cdot \int \frac{1}{x ( ln ( x ) ) ^{2}} d x

Apply u-substitution

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

= 4 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 4 (- \frac{1}{u})

Substitute back

u = ln (x)

= 4 (- \frac{1}{ln ( x )})

Simplify

4 (- \frac{1}{ln ( x )}) : - \frac{4}{ln ( x )}

= - \frac{4}{ln ( x )}

Add a constant to the solution

= - \frac{4}{ln ( x )} + C

x^{4} - 3 x^{2} + 9

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

\int (x + 6) (x - 5) d x

\frac{d}{d x} (sin (tan (cos (2 π x^{4}))))

x \to - \infty lim (x ln (x))

What is the integral of 4/(x(ln(x))^2) ?
The integral of 4/(x(ln(x))^2) is -4/(ln(x))+C