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

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

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integral of (x^4+3x^3-2x^2-5x)

\int (x^{4} + 3 x^{3} - 2 x^{2} - 5 x) d x

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

Solution steps

\int x^{4} + 3 x^{3} - 2 x^{2} - 5 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 x^{4} d x + \int 3 x^{3} d x - \int 2 x^{2} d x - \int 5 x d x

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

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

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

\int 5 x d x = \frac{5 x ^{2}}{2}

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

Add a constant to the solution

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

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