Integrate: \(\dfrac{3x^2}{x^6+1}\)
\(\tan^{-1}(x^3)+C\)
Integrate: \(\dfrac{1}{\sqrt{1+4x^2}}\)
\(\dfrac{1}{2}\log\left|2x+\sqrt{1+4x^2}\right|+C\)
Integrate: \(\dfrac{1}{\sqrt{(2-x)^2+1}}\)
\(\log\left|\dfrac{1}{2-x+\sqrt{x^2-4x+5}}\right|+C\)
Integrate: \(\dfrac{1}{\sqrt{9-25x^2}}\)
\(\dfrac{1}{5}\sin^{-1}\left(\dfrac{5x}{3}\right)+C\)
Integrate: \(\dfrac{3x}{1+2x^4}\)
\(\dfrac{3}{2\sqrt{2}}\tan^{-1}(\sqrt{2}\,x^2)+C\)
Integrate: \(\dfrac{x^2}{1-x^6}\)
\(\dfrac{1}{6}\log\left|\dfrac{1+x^3}{1-x^3}\right|+C\)
Integrate: \(\dfrac{x-1}{\sqrt{x^2-1}}\)
\(\sqrt{x^2-1}-\log\left|x+\sqrt{x^2-1}\right|+C\)
Integrate: \(\dfrac{x^2}{\sqrt{x^6+a^6}}\)
\(\dfrac{1}{3}\log\left|x^3+\sqrt{x^6+a^6}\right|+C\)
Integrate: \(\dfrac{\sec^2 x}{\sqrt{\tan^2 x+4}}\)
\(\log\left|\tan x+\sqrt{\tan^2 x+4}\right|+C\)
Integrate: \(\dfrac{1}{\sqrt{x^2+2x+2}}\)
\(\log\left|x+1+\sqrt{x^2+2x+2}\right|+C\)
Integrate: \(\dfrac{1}{9x^2+6x+5}\)
\(\dfrac{1}{6}\tan^{-1}\left(\dfrac{3x+1}{2}\right)+C\)
Integrate: \(\dfrac{1}{\sqrt{7-6x-x^2}}\)
\(\sin^{-1}\left(\dfrac{x+3}{4}\right)+C\)
Integrate: \(\dfrac{1}{\sqrt{(x-1)(x-2)}}\)
\(\log\left|x-\dfrac{3}{2}+\sqrt{x^2-3x+2}\right|+C\)
Integrate: \(\dfrac{1}{\sqrt{8+3x-x^2}}\)
\(\sin^{-1}\left(\dfrac{2x-3}{\sqrt{41}}\right)+C\)
Integrate: \(\dfrac{1}{\sqrt{(x-a)(x-b)}}\)
\(\log\left|x-\dfrac{a+b}{2}+\sqrt{(x-a)(x-b)}\right|+C\)
Integrate: \(\dfrac{4x+1}{\sqrt{2x^2+x-3}}\)
\(2\sqrt{2x^2+x-3}+C\)
Integrate: \(\dfrac{x+2}{\sqrt{x^2-1}}\)
\(\sqrt{x^2-1}+2\log\left|x+\sqrt{x^2-1}\right|+C\)
Integrate: \(\dfrac{5x-2}{1+2x+3x^2}\)
\(\dfrac{5}{6}\log\left|3x^2+2x+1\right|-\dfrac{11}{3\sqrt{2}}\tan^{-1}\left(\dfrac{3x+1}{\sqrt{2}}\right)+C\)
Integrate: \(\dfrac{6x+7}{\sqrt{(x-5)(x-4)}}\)
\(6\sqrt{x^2-9x+20}+34\log\left|x-\dfrac{9}{2}+\sqrt{x^2-9x+20}\right|+C\)
Integrate: \(\dfrac{x+2}{\sqrt{4x-x^2}}\)
\(-\sqrt{4x-x^2}+4\sin^{-1}\left(\dfrac{x-2}{2}\right)+C\)
Integrate: \(\dfrac{x+2}{\sqrt{x^2+2x+3}}\)
\(\sqrt{x^2+2x+3}+\log\left|x+1+\sqrt{x^2+2x+3}\right|+C\)
Integrate: \(\dfrac{x+3}{x^2-2x-5}\)
\(\dfrac{1}{2}\log\left|x^2-2x-5\right|+\dfrac{2}{\sqrt{6}}\log\left|\dfrac{x-1-\sqrt{6}}{x-1+\sqrt{6}}\right|+C\)
Integrate: \(\dfrac{5x+3}{\sqrt{x^2+4x+10}}\)
\(5\sqrt{x^2+4x+10}-7\log\left|x+2+\sqrt{x^2+4x+10}\right|+C\)