What is the integral of (5/(t^2)-8t^6) ?

The integral of (5/(t^2)-8t^6) is -5/t-(8t^7)/7+C

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integral of (5/(t^2)-8t^6)

\int (\frac{5}{t ^{2}} - 8 t^{6}) d t

- \frac{5}{t} - \frac{8 t ^{7}}{7} + C

Solution steps

\int \frac{5}{t ^{2}} - 8 t^{6} 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{5}{t ^{2}} d t - \int 8 t^{6} d t

\int \frac{5}{t ^{2}} d t = - \frac{5}{t}

\int 8 t^{6} d t = \frac{8 t ^{7}}{7}

= - \frac{5}{t} - \frac{8 t ^{7}}{7}

Add a constant to the solution

= - \frac{5}{t} - \frac{8 t ^{7}}{7} + C

What is the integral of (5/(t^2)-8t^6) ?
The integral of (5/(t^2)-8t^6) is -5/t-(8t^7)/7+C