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

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

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

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

\frac{x ^{6}}{2} + x^{5} + \frac{x ^{4}}{2} + C

Solution steps

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

Expand

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

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

\int 3 x^{5} d x = \frac{x ^{6}}{2}

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

= \frac{x ^{6}}{2} + x^{5} + \frac{x ^{4}}{2}

Add a constant to the solution

= \frac{x ^{6}}{2} + x^{5} + \frac{x ^{4}}{2} + C

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