What is the integral of (4x^7-4x^3+x) ?

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

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integral of (4x^7-4x^3+x)

\int (4 x^{7} - 4 x^{3} + x) d x

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

Solution steps

\int 4 x^{7} - 4 x^{3} + x 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 4 x^{7} d x - \int 4 x^{3} d x + \int x d x

\int 4 x^{7} d x = \frac{x ^{8}}{2}

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

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

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

Add a constant to the solution

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

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