Question

Evaluate the indefinite integral of dx/(x^(2)sqrt(64-x^2).

My answer was (1/32)(x-1/(2sqrt(64-x^2))-arcsin(x/8) after a long trig substitution. The website I enter my answer in says that it's incorrect but mentions that "there is always more than one possibility." Can you help me?

Answer 1

\[\int\frac{dx}{x^2\sqrt{64-x^2}}\] is the problem?

Answer 2

The attachment is a copy of my work.

Answer 3

yes. that is the problem

Answer 4

oh you made a big mess of a simple integral...

Answer 5

\[\int\frac1{64\sin^2\theta}d\theta=\frac1{64}\int\csc^2\theta d\theta=-\frac1{64}\cot\theta+C\]noticing the trig identity will make your life much easier ;)

Answer 6

and for the record\[\frac1{1-\cos(2\theta)}\neq1-\frac1{\cos(2\theta)}\]

Answer 7

I see where you're going. So from (-1/64)\[cot theta\]+c. Writing it in terms of sin and cos for the sake of my substitution i get (-1/64) \[cos theta/sin theta\] + c resulting in (-1/64) \[sqrt{64-x^2}/x\] + c. But the website is telling me that my answer is not the most general solution.