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Popular >

integral of (p^5-3)^2

Solution

\int (p^{5} - 3)^{2} d p

Solution

\frac{p ^{11}}{11} - p^{6} + 9 p + C

Solution steps

\int (p^{5} - 3)^{2} d p

Expand

(p^{5} - 3)^{2} : p^{10} - 6 p^{5} + 9

= \int p^{10} - 6 p^{5} + 9 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^{10} d p - \int 6 p^{5} d p + \int 9 d p

\int p^{10} d p = \frac{p ^{11}}{11}

\int 6 p^{5} d p = p^{6}

\int 9 d p = 9 p

= \frac{p ^{11}}{11} - p^{6} + 9 p

Add a constant to the solution

= \frac{p ^{11}}{11} - p^{6} + 9 p + C

Popular Examples

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\int \frac{1}{csc ( x ) + cot ( x )} d x

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\int (4 x + 1) cos (\frac{x}{3}) d x

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\int \frac{3 x ^{2} + 9 x ^{4} - x}{x ^{2}} d x

integral of (x+5)/(x^2-2x-8)

\int \frac{x + 5}{x ^{2} - 2 x - 8} d x

integral of (sqrt(x)+4x-5)

\int (x + 4 x - 5) d x

Frequently Asked Questions (FAQ)

What is the integral of (p^5-3)^2 ?
The integral of (p^5-3)^2 is (p^{11})/(11)-p^6+9p+C