What is the integral of (5x^3-8t) ?

The integral of (5x^3-8t) is 5x^3t-4t^2+C

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integral of (5x^3-8t)

\int (5 x^{3} - 8 t) d t

5 x^{3} t - 4 t^{2} + C

Solution steps

\int 5 x^{3} - 8 t 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 5 x^{3} d t - \int 8 t d t

\int 5 x^{3} d t = 5 x^{3} t

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

= 5 x^{3} t - 4 t^{2}

Add a constant to the solution

= 5 x^{3} t - 4 t^{2} + C

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