What is the integral of 18x^8-25x^4+3x^2 ?

The integral of 18x^8-25x^4+3x^2 is 2x^9-5x^5+x^3+C

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integral of 18x^8-25x^4+3x^2

\int 18 x^{8} - 25 x^{4} + 3 x^{2} d x

2 x^{9} - 5 x^{5} + x^{3} + C

Solution steps

\int 18 x^{8} - 25 x^{4} + 3 x^{2} 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 18 x^{8} d x - \int 25 x^{4} d x + \int 3 x^{2} d x

\int 18 x^{8} d x = 2 x^{9}

\int 25 x^{4} d x = 5 x^{5}

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

= 2 x^{9} - 5 x^{5} + x^{3}

Add a constant to the solution

= 2 x^{9} - 5 x^{5} + x^{3} + C

x \to \infty lim (5 x + 6)

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What is the integral of 18x^8-25x^4+3x^2 ?
The integral of 18x^8-25x^4+3x^2 is 2x^9-5x^5+x^3+C