What is the integral of 8t^3-6t^{-2} ?

The integral of 8t^3-6t^{-2} is 2t^4+6/t+C

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integral of 8t^3-6t^{-2}

\int 8 t^{3} - 6 t^{- 2} d t

2 t^{4} + \frac{6}{t} + C

Solution steps

\int 8 t^{3} - 6 t^{- 2} d t

6 t^{- 2} = \frac{6}{t ^{2}}

= \int 8 t^{3} - \frac{6}{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 8 t^{3} d t - \int \frac{6}{t ^{2}} d t

\int 8 t^{3} d t = 2 t^{4}

\int \frac{6}{t ^{2}} d t = - \frac{6}{t}

= 2 t^{4} - (- \frac{6}{t})

Simplify

= 2 t^{4} + \frac{6}{t}

Add a constant to the solution

= 2 t^{4} + \frac{6}{t} + C

x \to 5 + lim (\frac{2}{x - 5})

\int (e^{x} - 1)^{3} d x

f (x) = sin (5 x^{2})

x \to 0 lim (e^{x (1 - s)})

\int x^{3} cos (6 x) d x

What is the integral of 8t^3-6t^{-2} ?
The integral of 8t^3-6t^{-2} is 2t^4+6/t+C