What is the integral of (3/t-2/(t^2)) ?

The integral of (3/t-2/(t^2)) is 3ln|t|+2/t+C

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integral of (3/t-2/(t^2))

\int (\frac{3}{t} - \frac{2}{t ^{2}}) d t

3 ln ∣ t ∣ + \frac{2}{t} + C

Solution steps

\int \frac{3}{t} - \frac{2}{t ^{2}} d t

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{3}{t} d t - \int \frac{2}{t ^{2}} d t

\int \frac{3}{t} d t = 3 ln ∣ t ∣

\int \frac{2}{t ^{2}} d t = - \frac{2}{t}

= 3 ln ∣ t ∣ - (- \frac{2}{t})

Simplify

= 3 ln ∣ t ∣ + \frac{2}{t}

Add a constant to the solution

= 3 ln ∣ t ∣ + \frac{2}{t} + C

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What is the integral of (3/t-2/(t^2)) ?
The integral of (3/t-2/(t^2)) is 3ln|t|+2/t+C