What is the integral of (x^2)/2-x^4+602.5 ?

The integral of (x^2)/2-x^4+602.5 is 0.16666…x^3-0.2x^5+602.5x+C

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integral of (x^2)/2-x^4+602.5

\int \frac{x ^{2}}{2} - x^{4} + 602.5 d x

0.16666 \dots x^{3} - 0.2 x^{5} + 602.5 x + C

Solution steps

\int \frac{x ^{2}}{2} - x^{4} + 602.5 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 \frac{x ^{2}}{2} d x - \int x^{4} d x + \int 602.5 d x

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

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

\int 602.5 d x = 602.5 x

= \frac{x ^{3}}{6} - \frac{x ^{5}}{5} + 602.5 x

Simplify

= 0.16666 \dots x^{3} - 0.2 x^{5} + 602.5 x

Add a constant to the solution

= 0.16666 \dots x^{3} - 0.2 x^{5} + 602.5 x + C

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What is the integral of (x^2)/2-x^4+602.5 ?
The integral of (x^2)/2-x^4+602.5 is 0.16666…x^3-0.2x^5+602.5x+C