$$ 45.\,\int\!\! \frac{dx}{\sqrt{x^2-a^2}}= \frac{x}{\vert x \vert} arch \frac{\vert x \vert}{a}+C_1= ln \vert x+ \sqrt{x^2-a^2} \vert +C $$

$$ 46.\,\int\!\! \frac{dx}{\sqrt{(x^2-a^2)^3}}= - \frac{x}{a^2\sqrt{x^2-a^2}} +C $$

$$ 47.\,\int\!\! \frac{x}{\sqrt{x^2-a^2}}dx = \sqrt{x^2-a^2}+C $$

$$ 48.\,\int\!\! \frac{x}{\sqrt{(x^2-a^2)^3}}dx = - \frac{1}{\sqrt{x^2-a^2}} +C $$

$$ 49.\,\int\!\! \frac{x^2}{\sqrt{x^2-a^2}}dx =\frac{x}{2}\sqrt{x^2 -a ^2} + \frac{a^2}{2} \ln \vert x+ \sqrt{x^2-a^2} \vert +C $$

$$ 50.\,\int\!\! \frac{x^2}{\sqrt{(x^2-a^2)^3}}dx =-\frac{x}{\sqrt{x^2 -a ^2}} + \ln \vert x+ \sqrt{x^2-a^2} \vert +C $$

$$ 51.\,\int\!\! \frac{dx}{x\sqrt{x^2-a^2}}= \frac{1}{a} \arccos \frac{a}{\vert x \vert} +C $$

$$ 52.\,\int\!\! \frac{dx}{x^2\sqrt{x^2-a^2}} =\frac{ \sqrt {x^2-a^2}}{a^2x}+C $$

$$ 53.\,\int\!\! \sqrt{x^2-a^2}dx = \frac{x}{2} \sqrt{x^2-a^2} - \frac{a^2}{2} \ln \vert x+ \sqrt{x^2-a^2} \vert +C $$

$$ 54.\,\int\!\! \sqrt{(x^2-a^2)^3}dx =\frac{x}{8}(2x^2-5a^2)\sqrt{x^2-a^2} + \frac{3}{8} a^4 \ln \vert x+ \sqrt{x^2-a^2} \vert +C $$

$$ 55.\,\int\!\! x \sqrt{x^2-a^2}dx= \frac{1}{3}\sqrt{(x^2-a^2)^3} +C $$

$$ 56.\,\int\!\! x^2 \sqrt{x^2-a^2} dx = \frac{x}{8} (2x^2-a^2)\sqrt{x^2-a^2}-\frac{a^4}{8}\ln \vert x+ \sqrt{x^2-a^2} \vert +C $$

$$ 57.\,\int\!\! \frac{\sqrt{x^2-a^2}}{x} dx= \sqrt{x^2-a^2}- \arccos \frac{a}{\vert x \vert} +C $$

$$ 58.\,\int\!\! \frac{\sqrt{x^2-a^2}}{x^2} dx = -\frac{\sqrt{x^2-a^2}}{x} + \ln \vert x + \sqrt{x^2-a^2} \vert +C $$