What is the integral of 2x-2x^5+7x^3 ?

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

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integral of 2x-2x^5+7x^3

\int 2 x - 2 x^{5} + 7 x^{3} d x

x^{2} - \frac{x ^{6}}{3} + \frac{7 x ^{4}}{4} + C

Solution steps

\int 2 x - 2 x^{5} + 7 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 2 x d x - \int 2 x^{5} d x + \int 7 x^{3} d x

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

\int 2 x^{5} d x = \frac{x ^{6}}{3}

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

= x^{2} - \frac{x ^{6}}{3} + \frac{7 x ^{4}}{4}

Add a constant to the solution

= x^{2} - \frac{x ^{6}}{3} + \frac{7 x ^{4}}{4} + C

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