What is the integral of (x^4-5x+1) ?

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

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integral of (x^4-5x+1)

\int (x^{4} - 5 x + 1) d x

\frac{x ^{5}}{5} - \frac{5 x ^{2}}{2} + x + C

Solution steps

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

\int x^{4} d x = \frac{x ^{5}}{5}

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

\int 1 d x = x

= \frac{x ^{5}}{5} - \frac{5 x ^{2}}{2} + x

Add a constant to the solution

= \frac{x ^{5}}{5} - \frac{5 x ^{2}}{2} + x + C

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