What is the integral of (e^y-6/y) ?

The integral of (e^y-6/y) is e^y-6ln|y|+C

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integral of (e^y-6/y)

\int (e^{y} - \frac{6}{y}) d y

e^{y} - 6 ln ∣ y ∣ + C

Solution steps

\int e^{y} - \frac{6}{y} 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 e^{y} d y - \int \frac{6}{y} d y

\int e^{y} d y = e^{y}

\int \frac{6}{y} d y = 6 ln ∣ y ∣

= e^{y} - 6 ln ∣ y ∣

Add a constant to the solution

= e^{y} - 6 ln ∣ y ∣ + C

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