What is the integral of (1+ln(x))/((zln(x))^2) ?

The integral of (1+ln(x))/((zln(x))^2) is -(1+ln(x))/(zln^2(x))+C

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integral of (1+ln(x))/((zln(x))^2)

\int \frac{1 + ln ( x )}{( z ln ( x ) ) ^{2}} d z

- \frac{1 + ln ( x )}{z ln ^{2} ( x )} + C

Solution steps

\int \frac{1 + ln ( x )}{( z ln ( x ) ) ^{2}} d z

Take the constant out:

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

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

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

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

Simplify

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

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

Add a constant to the solution

= - \frac{1 + ln ( x )}{z ln ^{2} ( x )} + C

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What is the integral of (1+ln(x))/((zln(x))^2) ?
The integral of (1+ln(x))/((zln(x))^2) is -(1+ln(x))/(zln^2(x))+C