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Match each indefinite integral on the left with the corresponding functions on the right.

Remember: to verify $\displaystyle\int f(x)\,dx = F(x) + C$ , all you have to do is verify that $\displaystyle\frac{d}{dx}[F(x)] = f(x)$ .

Because this is a matching problem, WeBWorK will not tell you which answers are right and which are wrong. You must get all of the answers correct to get credit for the problem. There is no partial credit.

1. $\displaystyle\int x\sqrt{x^2 - 9} \, dx$
2. $\displaystyle\int x\sqrt{x^2 + 9} \, dx$
3. $\displaystyle\int \frac{1}{\sqrt{6 x - x^2}}\,dx$
4. $\displaystyle\int \frac{1}{(9 - x^2)^{3/2}}\,dx$

A. $\displaystyle\frac{x}{9\sqrt{9 - x^2}} + C$
B. $\displaystyle\arcsin\left( \frac{x-3}{3} \right) + C$
C. $\displaystyle\frac{1}{3}(x^2 - 9)^{3/2} + C$
D. $\displaystyle\frac{1}{3}(x^2 + 9)^{3/2} + C$

In order to get credit for this problem all answers must be correct.