What is the integral of-45t^{2/3}-80 ?

The integral of-45t^{2/3}-80 is -27t^{5/3}-80t+C

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integral of-45t^{2/3}-80

\int - 45 t^{\frac{2}{3}} - 80 d t

- 27 t^{\frac{5}{3}} - 80 t + C

Solution steps

\int - 45 t^{\frac{2}{3}} - 80 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 45 t^{\frac{2}{3}} d t - \int 80 d t

\int 45 t^{\frac{2}{3}} d t = 27 t^{\frac{5}{3}}

\int 80 d t = 80 t

= - 27 t^{\frac{5}{3}} - 80 t

Add a constant to the solution

= - 27 t^{\frac{5}{3}} - 80 t + C

\int_{0}^{\infty} 2 x e^{- 2 x} d x

\frac{d}{d x} (x x + 1)

\int (x^{2} + 5) cos (3 x) d x

f (x) = x^{3} cos (2 x)

x \frac{d y}{d x} = x^{3} + 9 x^{3} y

What is the integral of-45t^{2/3}-80 ?
The integral of-45t^{2/3}-80 is -27t^{5/3}-80t+C