CPM Homework Help : CALC3RD Problem 6-96

What is $\int x ^ { n } d x$ for $n = 3, 2, 1, 0, –1, –2, \text{ and } –3$ ? Then write a general formula for $\int x ^ { n } d x$ for $n ≠ -1$ .

Hint 1:

$\int x^{3}dx=\frac{x^{4}}{4}+C$

$\int x^{2}dx=\frac{x^{3}}{3}+C$

$\int xdx=\frac{x^{2}}{2}+C$

Keep going...

Hint 2:

A general formula will use the constant $n$ . Explain why $n = −1$ does not fit this pattern.