What is the integral of-6+10x^3-8x^5+6x^7 ?

The integral of-6+10x^3-8x^5+6x^7 is -6x+(5x^4)/2-(4x^6)/3+(3x^8)/4+C

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integral of-6+10x^3-8x^5+6x^7

\int - 6 + 10 x^{3} - 8 x^{5} + 6 x^{7} d x

- 6 x + \frac{5 x ^{4}}{2} - \frac{4 x ^{6}}{3} + \frac{3 x ^{8}}{4} + C

Solution steps

\int - 6 + 10 x^{3} - 8 x^{5} + 6 x^{7} 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 6 d x + \int 10 x^{3} d x - \int 8 x^{5} d x + \int 6 x^{7} d x

\int 6 d x = 6 x

\int 10 x^{3} d x = \frac{5 x ^{4}}{2}

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

\int 6 x^{7} d x = \frac{3 x ^{8}}{4}

= - 6 x + \frac{5 x ^{4}}{2} - \frac{4 x ^{6}}{3} + \frac{3 x ^{8}}{4}

Add a constant to the solution

= - 6 x + \frac{5 x ^{4}}{2} - \frac{4 x ^{6}}{3} + \frac{3 x ^{8}}{4} + C

What is the integral of-6+10x^3-8x^5+6x^7 ?
The integral of-6+10x^3-8x^5+6x^7 is -6x+(5x^4)/2-(4x^6)/3+(3x^8)/4+C