What is the integral of (8x^4-6x^2+10x-15) ?

The integral of (8x^4-6x^2+10x-15) is (8x^5)/5-2x^3+5x^2-15x+C

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integral of (8x^4-6x^2+10x-15)

\int (8 x^{4} - 6 x^{2} + 10 x - 15) d x

\frac{8 x ^{5}}{5} - 2 x^{3} + 5 x^{2} - 15 x + C

Solution steps

\int 8 x^{4} - 6 x^{2} + 10 x - 15 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 8 x^{4} d x - \int 6 x^{2} d x + \int 10 x d x - \int 15 d x

\int 8 x^{4} d x = \frac{8 x ^{5}}{5}

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

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

\int 15 d x = 15 x

= \frac{8 x ^{5}}{5} - 2 x^{3} + 5 x^{2} - 15 x

Add a constant to the solution

= \frac{8 x ^{5}}{5} - 2 x^{3} + 5 x^{2} - 15 x + C

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What is the integral of (8x^4-6x^2+10x-15) ?
The integral of (8x^4-6x^2+10x-15) is (8x^5)/5-2x^3+5x^2-15x+C