What is the integral of (1-2t^3)/(t^3) ?

The integral of (1-2t^3)/(t^3) is -1/(2t^2)-2t+C

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integral of (1-2t^3)/(t^3)

\int \frac{1 - 2 t ^{3}}{t ^{3}} d t

- \frac{1}{2 t ^{2}} - 2 t + C

Solution steps

\int \frac{1 - 2 t ^{3}}{t ^{3}} d t

Expand

\frac{1 - 2 t ^{3}}{t ^{3}} : \frac{1}{t ^{3}} - 2

= \int \frac{1}{t ^{3}} - 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{1}{t ^{3}} d t - \int 2 d t

\int \frac{1}{t ^{3}} d t = - \frac{1}{2 t ^{2}}

\int 2 d t = 2 t

= - \frac{1}{2 t ^{2}} - 2 t

Add a constant to the solution

= - \frac{1}{2 t ^{2}} - 2 t + C

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What is the integral of (1-2t^3)/(t^3) ?
The integral of (1-2t^3)/(t^3) is -1/(2t^2)-2t+C