What is the integral of (x^5-3x^4+6x^3+3) ?

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

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integral of (x^5-3x^4+6x^3+3)

\int (x^{5} - 3 x^{4} + 6 x^{3} + 3) d x

\frac{x ^{6}}{6} - \frac{3 x ^{5}}{5} + \frac{3 x ^{4}}{2} + 3 x + C

Solution steps

\int x^{5} - 3 x^{4} + 6 x^{3} + 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^{5} d x - \int 3 x^{4} d x + \int 6 x^{3} d x + \int 3 d x

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

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

\int 6 x^{3} d x = \frac{3 x ^{4}}{2}

\int 3 d x = 3 x

= \frac{x ^{6}}{6} - \frac{3 x ^{5}}{5} + \frac{3 x ^{4}}{2} + 3 x

Add a constant to the solution

= \frac{x ^{6}}{6} - \frac{3 x ^{5}}{5} + \frac{3 x ^{4}}{2} + 3 x + C

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