What is the integral of (x^{10}+x^4+4x^3) ?

The integral of (x^{10}+x^4+4x^3) is (x^{11}}{11}+\frac{x^5)/5+x^4+C

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integral of (x^{10}+x^4+4x^3)

\int (x^{10} + x^{4} + 4 x^{3}) d x

\frac{x ^{11}}{11} + \frac{x ^{5}}{5} + x^{4} + C

Solution steps

\int x^{10} + x^{4} + 4 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 x^{10} d x + \int x^{4} d x + \int 4 x^{3} d x

\int x^{10} d x = \frac{x ^{11}}{11}

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

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

= \frac{x ^{11}}{11} + \frac{x ^{5}}{5} + x^{4}

Add a constant to the solution

= \frac{x ^{11}}{11} + \frac{x ^{5}}{5} + x^{4} + C

What is the integral of (x^{10}+x^4+4x^3) ?
The integral of (x^{10}+x^4+4x^3) is (x^{11}}{11}+\frac{x^5)/5+x^4+C