What is the integral of (10x^4-18x^2+2x+3) ?

The integral of (10x^4-18x^2+2x+3) is 2x^5-6x^3+x^2+3x+C

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integral of (10x^4-18x^2+2x+3)

\int (10 x^{4} - 18 x^{2} + 2 x + 3) d x

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

Solution steps

\int 10 x^{4} - 18 x^{2} + 2 x + 3 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 10 x^{4} d x - \int 18 x^{2} d x + \int 2 x d x + \int 3 d x

\int 10 x^{4} d x = 2 x^{5}

\int 18 x^{2} d x = 6 x^{3}

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

What is the integral of (10x^4-18x^2+2x+3) ?
The integral of (10x^4-18x^2+2x+3) is 2x^5-6x^3+x^2+3x+C