What is the integral of+10t^{-3}+12t^{-9}+4t^3 ?

The integral of+10t^{-3}+12t^{-9}+4t^3 is -5/(t^2)-3/(2t^8)+t^4+C

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integral of+10t^{-3}+12t^{-9}+4t^3

\int + 10 t^{- 3} + 12 t^{- 9} + 4 t^{3} d t

- \frac{5}{t ^{2}} - \frac{3}{2 t ^{8}} + t^{4} + C

Solution steps

\int 10 t^{- 3} + 12 t^{- 9} + 4 t^{3} 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 10 t^{- 3} d t + \int 12 t^{- 9} d t + \int 4 t^{3} d t

\int 10 t^{- 3} d t = - \frac{5}{t ^{2}}

\int 12 t^{- 9} d t = - \frac{3}{2 t ^{8}}

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

= - \frac{5}{t ^{2}} - \frac{3}{2 t ^{8}} + t^{4}

Add a constant to the solution

= - \frac{5}{t ^{2}} - \frac{3}{2 t ^{8}} + t^{4} + C

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What is the integral of+10t^{-3}+12t^{-9}+4t^3 ?
The integral of+10t^{-3}+12t^{-9}+4t^3 is -5/(t^2)-3/(2t^8)+t^4+C