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

The integral of (5-3x)(2+x^2) is 10x+(5x^3)/3-3x^2-(3x^4)/4+C

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

integral

(5 - 3 x) (2 + x^{2})

10 x + \frac{5 x ^{3}}{3} - 3 x^{2} - \frac{3 x ^{4}}{4} + C

Solution steps

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

Expand

(5 - 3 x) (2 + x^{2}) : 10 + 5 x^{2} - 6 x - 3 x^{3}

= \int 10 + 5 x^{2} - 6 x - 3 x^{3} 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 10 d x + \int 5 x^{2} d x - \int 6 x d x - \int 3 x^{3} d x

\int 10 d x = 10 x

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

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

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

= 10 x + \frac{5 x ^{3}}{3} - 3 x^{2} - \frac{3 x ^{4}}{4}

Add a constant to the solution

= 10 x + \frac{5 x ^{3}}{3} - 3 x^{2} - \frac{3 x ^{4}}{4} + C

What is the integral of (5-3x)(2+x^2) ?
The integral of (5-3x)(2+x^2) is 10x+(5x^3)/3-3x^2-(3x^4)/4+C