$$ 59.\,\int\!\! \frac{dx}{\sqrt{a^2-x^2}} =\arcsin \frac{x}{a} +C $$

$$ 60.\,\int\!\! \frac{dx}{\sqrt{(a^2-x^2)^3}}= \frac{x}{a^2\sqrt{a^2-x^2}}+C $$

$$ 61.\,\int\!\! \frac{x}{\sqrt{a^2-x^2}} dx = - \sqrt{a^2-x^2}+C $$

$$ 62.\,\int\!\! \frac{x}{\sqrt{(a^2-x^2)^3}} dx = - \frac{1}{\sqrt{a^2-x^2}} +C $$

$$ 63.\,\int\!\! \frac{x^2}{\sqrt{a^2-x^2}}dx = -\frac{x}{2}\sqrt{a^2-x^2} + \frac{a^2}{2}\arcsin \frac{x}{a}+C $$

$$ 64.\,\int\!\! \frac{x^2}{\sqrt{(a^2-x^2)^3}}dx =\frac{x}{\sqrt{a^2-x^2}}- \arcsin \frac{x}{a} +C $$

$$ 65.\,\int\!\! \frac{dx}{x\sqrt{a^2-x^2}}=\frac{1}{a}\ln\frac{a-\sqrt{a^2-x^2}}{\vert x \vert } +C $$

$$ 66.\,\int\!\! \frac{dx}{x^2\sqrt{a^2-x^2}}=- \frac{a^2-x^2}{a^2x}+C $$

$$ 67.\,\int\!\! \sqrt{a^2-x^2}dx= \frac{x}{2} \sqrt{a^2-x^2} + \frac{a^2}{2}\arcsin \frac{x}{a}+C $$

$$ 68.\,\int\!\! \sqrt{(a^2-x^2)^3}dx=\frac{x}{8}(5a^2-2x^2)\sqrt{a^2-x^2}+\frac{3}{8}a^4\arcsin\frac{x}{a}+C $$

$$ 69.\,\int\!\! x\sqrt{a^2-x^2}dx=-\frac{1}{3}\sqrt{(a^2-x^2)^3}+C $$

$$ 70.\,\int\!\! x^2\sqrt{a^2-x^2}dx=\frac{x}{8}(2x^2-a^2)\sqrt{a^2-x^2}+\frac{a^4}{8}\arcsin\frac{x}{a}+C $$

$$ 71.\,\int\!\! \frac{\sqrt{a^2-x^2}}{x} dx =\sqrt{a^2-x^2}+a \ln \frac{a-\sqrt{a^2-x^2}}{\vert x \vert}+C $$

$$ 72.\,\int\!\! \frac{\sqrt{a^2-x^2}}{x^2}dx=-\frac{\sqrt{a^2-x^2}}{x}-\arcsin \frac{x}{a}+C $$