What is the integral of (3+x^4)(8+x^3) ?

The integral of (3+x^4)(8+x^3) is 24x+(3x^4)/4+(8x^5)/5+(x^8)/8+C

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integral of (3+x^4)(8+x^3)

\int (3 + x^{4}) (8 + x^{3}) d x

24 x + \frac{3 x ^{4}}{4} + \frac{8 x ^{5}}{5} + \frac{x ^{8}}{8} + C

Solution steps

\int (3 + x^{4}) (8 + x^{3}) d x

Expand

(3 + x^{4}) (8 + x^{3}) : 24 + 3 x^{3} + 8 x^{4} + x^{7}

= \int 24 + 3 x^{3} + 8 x^{4} + x^{7} 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 24 d x + \int 3 x^{3} d x + \int 8 x^{4} d x + \int x^{7} d x

\int 24 d x = 24 x

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

\int 8 x^{4} d x = \frac{8 x ^{5}}{5}

\int x^{7} d x = \frac{x ^{8}}{8}

= 24 x + \frac{3 x ^{4}}{4} + \frac{8 x ^{5}}{5} + \frac{x ^{8}}{8}

Add a constant to the solution

= 24 x + \frac{3 x ^{4}}{4} + \frac{8 x ^{5}}{5} + \frac{x ^{8}}{8} + C

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What is the integral of (3+x^4)(8+x^3) ?
The integral of (3+x^4)(8+x^3) is 24x+(3x^4)/4+(8x^5)/5+(x^8)/8+C