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

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

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integral of (8x^5-5x^4-3x^3+6x^2-10x-5)

\int (8 x^{5} - 5 x^{4} - 3 x^{3} + 6 x^{2} - 10 x - 5) d x

\frac{4 x ^{6}}{3} - x^{5} - \frac{3 x ^{4}}{4} + 2 x^{3} - 5 x^{2} - 5 x + C

Solution steps

\int 8 x^{5} - 5 x^{4} - 3 x^{3} + 6 x^{2} - 10 x - 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 8 x^{5} d x - \int 5 x^{4} d x - \int 3 x^{3} d x + \int 6 x^{2} d x - \int 10 x d x - \int 5 d x

\int 8 x^{5} d x = \frac{4 x ^{6}}{3}

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

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

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

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

\int 5 d x = 5 x

= \frac{4 x ^{6}}{3} - x^{5} - \frac{3 x ^{4}}{4} + 2 x^{3} - 5 x^{2} - 5 x

Add a constant to the solution

= \frac{4 x ^{6}}{3} - x^{5} - \frac{3 x ^{4}}{4} + 2 x^{3} - 5 x^{2} - 5 x + C

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