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

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

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integral of (5x^5-3x^3-x)

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

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

Solution steps

\int 5 x^{5} - 3 x^{3} - x 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 5 x^{5} d x - \int 3 x^{3} d x - \int x d x

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

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

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

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

Add a constant to the solution

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

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