What is the integral of 1-x-4x^3+2x^5 ?

The integral of 1-x-4x^3+2x^5 is x-(x^2)/2-x^4+(x^6)/3+C

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integral of 1-x-4x^3+2x^5

\int 1 - x - 4 x^{3} + 2 x^{5} d x

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

Solution steps

\int 1 - x - 4 x^{3} + 2 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 1 d x - \int x d x - \int 4 x^{3} d x + \int 2 x^{5} d x

\int 1 d x = x

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

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

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

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

Add a constant to the solution

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

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What is the integral of 1-x-4x^3+2x^5 ?
The integral of 1-x-4x^3+2x^5 is x-(x^2)/2-x^4+(x^6)/3+C