What is the integral of (24x^5-12x^3-x+2) ?

The integral of (24x^5-12x^3-x+2) is 4x^6-3x^4-(x^2)/2+2x+C

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integral of (24x^5-12x^3-x+2)

\int (24 x^{5} - 12 x^{3} - x + 2) d x

4 x^{6} - 3 x^{4} - \frac{x ^{2}}{2} + 2 x + C

Solution steps

\int 24 x^{5} - 12 x^{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 24 x^{5} d x - \int 12 x^{3} d x - \int x d x + \int 2 d x

\int 24 x^{5} d x = 4 x^{6}

\int 12 x^{3} d x = 3 x^{4}

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

\int 2 d x = 2 x

= 4 x^{6} - 3 x^{4} - \frac{x ^{2}}{2} + 2 x

Add a constant to the solution

= 4 x^{6} - 3 x^{4} - \frac{x ^{2}}{2} + 2 x + C

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\int \frac{9}{( x - 3 ) ^{2}} d x

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What is the integral of (24x^5-12x^3-x+2) ?
The integral of (24x^5-12x^3-x+2) is 4x^6-3x^4-(x^2)/2+2x+C