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

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

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integral of 2p^3-5p+1

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

\frac{p ^{4}}{2} - \frac{5 p ^{2}}{2} + p + C

Solution steps

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

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 p^{3} d p - \int 5 p d p + \int 1 d p

\int 2 p^{3} d p = \frac{p ^{4}}{2}

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

\int 1 d p = p

= \frac{p ^{4}}{2} - \frac{5 p ^{2}}{2} + p

Add a constant to the solution

= \frac{p ^{4}}{2} - \frac{5 p ^{2}}{2} + p + C

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