What is the integral of x/y+ln(z) ?

The integral of x/y+ln(z) is xln|y|+ln(z)y+C

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integral of x/y+ln(z)

\int \frac{x}{y} + ln (z) d y

x ln ∣ y ∣ + ln (z) y + C

Solution steps

\int \frac{x}{y} + ln (z) d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{x}{y} d y + \int ln (z) d y

\int \frac{x}{y} d y = x ln ∣ y ∣

\int ln (z) d y = ln (z) y

= x ln ∣ y ∣ + ln (z) y

Add a constant to the solution

= x ln ∣ y ∣ + ln (z) y + C

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What is the integral of x/y+ln(z) ?
The integral of x/y+ln(z) is xln|y|+ln(z)y+C