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Exponents with Unlike Bases and Same Exponent

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Question

Evaluate $\int r^{4} (7 - \frac{r^{5}}{10}) d r$

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Solution

$I = \int r^{4} (7 - \frac{r^{5}}{10}) d r$

$= \int (7 r^{4} - \frac{r^{9}}{10}) d r$

$= 7 \int r^{4} d r - \frac{1}{10} \int r^{9} d r$

$= \frac{7}{5} r^{5} - \frac{1}{100} r^{10} + c$ .

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