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

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

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

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

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

Solution steps

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

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

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