What is the integral of (5/4 x^4-(x^2)/2-4) ?

The integral of (5/4 x^4-(x^2)/2-4) is (x^5)/4-(x^3)/6-4x+C

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integral of (5/4 x^4-(x^2)/2-4)

\int (\frac{5}{4} x^{4} - \frac{x ^{2}}{2} - 4) d x

\frac{x ^{5}}{4} - \frac{x ^{3}}{6} - 4 x + C

Solution steps

\int \frac{5}{4} x^{4} - \frac{x ^{2}}{2} - 4 d x

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}{4} x^{4} d x - \int \frac{x ^{2}}{2} d x - \int 4 d x

\int \frac{5}{4} x^{4} d x = \frac{x ^{5}}{4}

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

\int 4 d x = 4 x

= \frac{x ^{5}}{4} - \frac{x ^{3}}{6} - 4 x

Add a constant to the solution

= \frac{x ^{5}}{4} - \frac{x ^{3}}{6} - 4 x + C

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What is the integral of (5/4 x^4-(x^2)/2-4) ?
The integral of (5/4 x^4-(x^2)/2-4) is (x^5)/4-(x^3)/6-4x+C