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

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

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integral of (t^2+2)/(t^2)

\int \frac{t ^{2} + 2}{t ^{2}} d t

t - \frac{2}{t} + C

Solution steps

\int \frac{t ^{2} + 2}{t ^{2}} d t

Expand

\frac{t ^{2} + 2}{t ^{2}} : 1 + \frac{2}{t ^{2}}

= \int 1 + \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 1 d t + \int \frac{2}{t ^{2}} d t

\int 1 d t = t

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

= t - \frac{2}{t}

Add a constant to the solution

= t - \frac{2}{t} + C

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