What is the integral of p+p^2+p^3+sqrt(p)+p^{3/2} ?

The integral of p+p^2+p^3+sqrt(p)+p^{3/2} is (p^2)/2+(p^3)/3+(p^4)/4+2/3 p^{3/2}+2/5 p^{5/2}+C

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integral of p+p^2+p^3+sqrt(p)+p^{3/2}

\int p + p^{2} + p^{3} + p + p^{\frac{3}{2}} d p

\frac{p ^{2}}{2} + \frac{p ^{3}}{3} + \frac{p ^{4}}{4} + \frac{2}{3} p^{\frac{3}{2}} + \frac{2}{5} p^{\frac{5}{2}} + C

Solution steps

\int p + p^{2} + p^{3} + p + p^{\frac{3}{2}} 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 p d p + \int p^{2} d p + \int p^{3} d p + \int p d p + \int p^{\frac{3}{2}} d p

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

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

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

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

\int p^{\frac{3}{2}} d p = \frac{2}{5} p^{\frac{5}{2}}

= \frac{p ^{2}}{2} + \frac{p ^{3}}{3} + \frac{p ^{4}}{4} + \frac{2}{3} p^{\frac{3}{2}} + \frac{2}{5} p^{\frac{5}{2}}

Add a constant to the solution

= \frac{p ^{2}}{2} + \frac{p ^{3}}{3} + \frac{p ^{4}}{4} + \frac{2}{3} p^{\frac{3}{2}} + \frac{2}{5} p^{\frac{5}{2}} + C

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What is the integral of p+p^2+p^3+sqrt(p)+p^{3/2} ?
The integral of p+p^2+p^3+sqrt(p)+p^{3/2} is (p^2)/2+(p^3)/3+(p^4)/4+2/3 p^{3/2}+2/5 p^{5/2}+C