What is the integral of x^7-2x^5+2x^5+x-1 ?

The integral of x^7-2x^5+2x^5+x-1 is (x^8)/8+(x^2)/2-x+C

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integral of x^7-2x^5+2x^5+x-1

integral

x^{7} - 2 x^{5} + 2 x^{5} + x - 1

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

Solution steps

\int x^{7} - 2 x^{5} + 2 x^{5} + x - 1 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 x^{7} d x - \int 2 x^{5} d x + \int 2 x^{5} d x + \int x d x - \int 1 d x

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

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

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

\int 1 d x = x

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

Simplify

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

Add a constant to the solution

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

What is the integral of x^7-2x^5+2x^5+x-1 ?
The integral of x^7-2x^5+2x^5+x-1 is (x^8)/8+(x^2)/2-x+C