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

The integral of (5+x^3)(4-x^2) is 20x-(5x^3)/3+x^4-(x^6)/6+C

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integral of (5+x^3)(4-x^2)

\int (5 + x^{3}) (4 - x^{2}) d x

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

Solution steps

\int (5 + x^{3}) (4 - x^{2}) d x

Expand

(5 + x^{3}) (4 - x^{2}) : 20 - 5 x^{2} + 4 x^{3} - x^{5}

= \int 20 - 5 x^{2} + 4 x^{3} - x^{5} 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 20 d x - \int 5 x^{2} d x + \int 4 x^{3} d x - \int x^{5} d x

\int 20 d x = 20 x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

\int x^{5} d x = \frac{x ^{6}}{6}

= 20 x - \frac{5 x ^{3}}{3} + x^{4} - \frac{x ^{6}}{6}

Add a constant to the solution

= 20 x - \frac{5 x ^{3}}{3} + x^{4} - \frac{x ^{6}}{6} + C

What is the integral of (5+x^3)(4-x^2) ?
The integral of (5+x^3)(4-x^2) is 20x-(5x^3)/3+x^4-(x^6)/6+C