What is the integral of (2x^{11}+x^5)(x^{12}+x^6) ?

The integral of (2x^{11}+x^5)(x^{12}+x^6) is (x^{24}}{12}+(x^{18})/6+\frac{x^{12})/(12)+C

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integral of (2x^{11}+x^5)(x^{12}+x^6)

\int (2 x^{11} + x^{5}) (x^{12} + x^{6}) d x

\frac{x ^{24}}{12} + \frac{x ^{18}}{6} + \frac{x ^{12}}{12} + C

Solution steps

\int (2 x^{11} + x^{5}) (x^{12} + x^{6}) d x

Expand

(2 x^{11} + x^{5}) (x^{12} + x^{6}) : 2 x^{23} + 3 x^{17} + x^{11}

= \int 2 x^{23} + 3 x^{17} + x^{11} 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 2 x^{23} d x + \int 3 x^{17} d x + \int x^{11} d x

\int 2 x^{23} d x = \frac{x ^{24}}{12}

\int 3 x^{17} d x = \frac{x ^{18}}{6}

\int x^{11} d x = \frac{x ^{12}}{12}

= \frac{x ^{24}}{12} + \frac{x ^{18}}{6} + \frac{x ^{12}}{12}

Add a constant to the solution

= \frac{x ^{24}}{12} + \frac{x ^{18}}{6} + \frac{x ^{12}}{12} + C

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What is the integral of (2x^{11}+x^5)(x^{12}+x^6) ?
The integral of (2x^{11}+x^5)(x^{12}+x^6) is (x^{24}}{12}+(x^{18})/6+\frac{x^{12})/(12)+C