What is the integral of (x^4+2x^3-5x+9) ?

The integral of (x^4+2x^3-5x+9) is (x^5)/5+(x^4)/2-(5x^2)/2+9x+C

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integral of (x^4+2x^3-5x+9)

\int (x^{4} + 2 x^{3} - 5 x + 9) d x

\frac{x ^{5}}{5} + \frac{x ^{4}}{2} - \frac{5 x ^{2}}{2} + 9 x + C

Solution steps

\int x^{4} + 2 x^{3} - 5 x + 9 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 2 x^{3} d x - \int 5 x d x + \int 9 d x

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

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

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

\int 9 d x = 9 x

= \frac{x ^{5}}{5} + \frac{x ^{4}}{2} - \frac{5 x ^{2}}{2} + 9 x

Add a constant to the solution

= \frac{x ^{5}}{5} + \frac{x ^{4}}{2} - \frac{5 x ^{2}}{2} + 9 x + C

What is the integral of (x^4+2x^3-5x+9) ?
The integral of (x^4+2x^3-5x+9) is (x^5)/5+(x^4)/2-(5x^2)/2+9x+C