What is the integral of 9/(x(ln(x))^2) ?

The integral of 9/(x(ln(x))^2) is -9/(ln(x))+C

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integral of 9/(x(ln(x))^2)

\int \frac{9}{x ( ln ( x ) ) ^{2}} d x

- \frac{9}{ln ( x )} + C

Solution steps

\int \frac{9}{x ( ln ( x ) ) ^{2}} d x

Take the constant out:

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

= 9 \cdot \int \frac{1}{x ( ln ( x ) ) ^{2}} d x

Apply u-substitution

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

= 9 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 9 (- \frac{1}{u})

Substitute back

u = ln (x)

= 9 (- \frac{1}{ln ( x )})

Simplify

9 (- \frac{1}{ln ( x )}) : - \frac{9}{ln ( x )}

= - \frac{9}{ln ( x )}

Add a constant to the solution

= - \frac{9}{ln ( x )} + C

x \to 0 lim (x (cot (2 x)))

x, x^{2}

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

f (x) = 5 x + 6, at x = 2

x \frac{d y}{d x} + 2 y = 8 x^{2}

What is the integral of 9/(x(ln(x))^2) ?
The integral of 9/(x(ln(x))^2) is -9/(ln(x))+C