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

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

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

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

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

Solution steps

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

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

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

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

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