3.5.1 \(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x}+\sqrt {c+b x}} \, dx\) [401]
3.5.2 \(\int \genfrac {}{}{}{}{x}{\sqrt {a+b x}+\sqrt {c+b x}} \, dx\) [402]
3.5.3 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b x}+\sqrt {c+b x}} \, dx\) [403]
3.5.4 \(\int \genfrac {}{}{}{}{1}{x (\sqrt {a+b x}+\sqrt {c+b x})} \, dx\) [404]
3.5.5 \(\int \genfrac {}{}{}{}{1}{x^2 (\sqrt {a+b x}+\sqrt {c+b x})} \, dx\) [405]
3.5.6 \(\int \genfrac {}{}{}{}{x^2}{(\sqrt {a+b x}+\sqrt {c+b x})^2} \, dx\) [406]
3.5.7 \(\int \genfrac {}{}{}{}{x}{(\sqrt {a+b x}+\sqrt {c+b x})^2} \, dx\) [407]
3.5.8 \(\int \genfrac {}{}{}{}{1}{(\sqrt {a+b x}+\sqrt {c+b x})^2} \, dx\) [408]
3.5.9 \(\int \genfrac {}{}{}{}{1}{x (\sqrt {a+b x}+\sqrt {c+b x})^2} \, dx\) [409]
3.5.10 \(\int \genfrac {}{}{}{}{1}{x^2 (\sqrt {a+b x}+\sqrt {c+b x})^2} \, dx\) [410]
3.5.11 \(\int \genfrac {}{}{}{}{x^2}{(\sqrt {a+b x}+\sqrt {c+b x})^3} \, dx\) [411]
3.5.12 \(\int \genfrac {}{}{}{}{x}{(\sqrt {a+b x}+\sqrt {c+b x})^3} \, dx\) [412]
3.5.13 \(\int \genfrac {}{}{}{}{1}{(\sqrt {a+b x}+\sqrt {c+b x})^3} \, dx\) [413]
3.5.14 \(\int \genfrac {}{}{}{}{1}{x (\sqrt {a+b x}+\sqrt {c+b x})^3} \, dx\) [414]
3.5.15 \(\int \genfrac {}{}{}{}{1}{x^2 (\sqrt {a+b x}+\sqrt {c+b x})^3} \, dx\) [415]
3.5.16 \(\int \genfrac {}{}{}{}{1}{\sqrt {x}+\sqrt {1+x}} \, dx\) [416]
3.5.17 \(\int \genfrac {}{}{}{}{1}{\sqrt {-1+x}+\sqrt {x}} \, dx\) [417]
3.5.18 \(\int \genfrac {}{}{}{}{1}{\sqrt {-1+x}+\sqrt {1+x}} \, dx\) [418]
3.5.19 \(\int x^3 (\sqrt {1-x}+\sqrt {1+x})^2 \, dx\) [419]
3.5.20 \(\int x^2 (\sqrt {1-x}+\sqrt {1+x})^2 \, dx\) [420]
3.5.21 \(\int x (\sqrt {1-x}+\sqrt {1+x})^2 \, dx\) [421]
3.5.22 \(\int (\sqrt {1-x}+\sqrt {1+x})^2 \, dx\) [422]
3.5.23 \(\int \genfrac {}{}{}{}{(\sqrt {1-x}+\sqrt {1+x})^2}{x} \, dx\) [423]
3.5.24 \(\int \genfrac {}{}{}{}{(\sqrt {1-x}+\sqrt {1+x})^2}{x^2} \, dx\) [424]
3.5.25 \(\int \genfrac {}{}{}{}{(\sqrt {1-x}+\sqrt {1+x})^2}{x^3} \, dx\) [425]
3.5.26 \(\int \genfrac {}{}{}{}{x^3}{\sqrt {a+b x}+\sqrt {a+c x}} \, dx\) [426]
3.5.27 \(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x}+\sqrt {a+c x}} \, dx\) [427]
3.5.28 \(\int \genfrac {}{}{}{}{x}{\sqrt {a+b x}+\sqrt {a+c x}} \, dx\) [428]
3.5.29 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b x}+\sqrt {a+c x}} \, dx\) [429]
3.5.30 \(\int \genfrac {}{}{}{}{1}{x (\sqrt {a+b x}+\sqrt {a+c x})} \, dx\) [430]
3.5.31 \(\int \genfrac {}{}{}{}{1}{x^2 (\sqrt {a+b x}+\sqrt {a+c x})} \, dx\) [431]
3.5.32 \(\int \genfrac {}{}{}{}{x^3}{(\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\) [432]
3.5.33 \(\int \genfrac {}{}{}{}{x^2}{(\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\) [433]
3.5.34 \(\int \genfrac {}{}{}{}{x}{(\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\) [434]
3.5.35 \(\int \genfrac {}{}{}{}{1}{(\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\) [435]
3.5.36 \(\int \genfrac {}{}{}{}{1}{x (\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\) [436]
3.5.37 \(\int \genfrac {}{}{}{}{1}{x^2 (\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\) [437]
3.5.38 \(\int \genfrac {}{}{}{}{x^4}{(\sqrt {a+b x}+\sqrt {a+c x})^3} \, dx\) [438]
3.5.39 \(\int \genfrac {}{}{}{}{x^3}{(\sqrt {a+b x}+\sqrt {a+c x})^3} \, dx\) [439]
3.5.40 \(\int \genfrac {}{}{}{}{x^2}{(\sqrt {a+b x}+\sqrt {a+c x})^3} \, dx\) [440]
3.5.41 \(\int \genfrac {}{}{}{}{x}{(\sqrt {a+b x}+\sqrt {a+c x})^3} \, dx\) [441]
3.5.42 \(\int \genfrac {}{}{}{}{1}{(\sqrt {a+b x}+\sqrt {a+c x})^3} \, dx\) [442]
3.5.43 \(\int \sqrt {1-x} (\sqrt {1-x}+\sqrt {1+x}) \, dx\) [443]
3.5.44 \(\int x^3 (-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x}) \, dx\) [444]
3.5.45 \(\int x^2 (-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x}) \, dx\) [445]
3.5.46 \(\int x (-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x}) \, dx\) [446]
3.5.47 \(\int (-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x}) \, dx\) [447]
3.5.48 \(\int \genfrac {}{}{}{}{(-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x})}{x} \, dx\) [448]
3.5.49 \(\int \genfrac {}{}{}{}{(-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x})}{x^2} \, dx\) [449]
3.5.50 \(\int \genfrac {}{}{}{}{(-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x})}{x^3} \, dx\) [450]
3.5.51 \(\int \genfrac {}{}{}{}{\sqrt {1-x}+\sqrt {1+x}}{-\sqrt {1-x}+\sqrt {1+x}} \, dx\) [451]
3.5.52 \(\int \genfrac {}{}{}{}{-\sqrt {-1+x}+\sqrt {1+x}}{\sqrt {-1+x}+\sqrt {1+x}} \, dx\) [452]
3.5.53 \(\int (d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [453]
3.5.54 \(\int (d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^3 \, dx\) [454]
3.5.55 \(\int (d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^2 \, dx\) [455]
3.5.56 \(\int (d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}}) \, dx\) [456]
3.5.57 \(\int \genfrac {}{}{}{}{1}{d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}}} \, dx\) [457]
3.5.58 \(\int \genfrac {}{}{}{}{1}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^2} \, dx\) [458]
3.5.59 \(\int \genfrac {}{}{}{}{1}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^3} \, dx\) [459]
3.5.60 \(\int (d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^{5/2} \, dx\) [460]
3.5.61 \(\int (d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^{3/2} \, dx\) [461]
3.5.62 \(\int \sqrt {d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}}} \, dx\) [462]
3.5.63 \(\int \genfrac {}{}{}{}{1}{\sqrt {d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}}}} \, dx\) [463]
3.5.64 \(\int \genfrac {}{}{}{}{1}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^{3/2}} \, dx\) [464]
3.5.65 \(\int \genfrac {}{}{}{}{1}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^{5/2}} \, dx\) [465]
3.5.66 \(\int \sqrt {x-\sqrt {-4+x^2}} \, dx\) [466]
3.5.67 \(\int \sqrt {a x+b \sqrt {c+\genfrac {}{}{}{}{a^2 x^2}{b^2}}} \, dx\) [467]
3.5.68 \(\int \sqrt {1+\sqrt {1-x^2}} \, dx\) [468]
3.5.69 \(\int \sqrt {1+\sqrt {1+x^2}} \, dx\) [469]
3.5.70 \(\int \sqrt {5+\sqrt {25+x^2}} \, dx\) [470]
3.5.71 \(\int \sqrt {a+b \sqrt {\genfrac {}{}{}{}{a^2}{b^2}+c x^2}} \, dx\) [471]
3.5.72 \(\int (d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [472]
3.5.73 \(\int (d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^3 \, dx\) [473]
3.5.74 \(\int (d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^2 \, dx\) [474]
3.5.75 \(\int (d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}}) \, dx\) [475]
3.5.76 \(\int \genfrac {}{}{}{}{1}{d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}}} \, dx\) [476]
3.5.77 \(\int \genfrac {}{}{}{}{1}{(d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^2} \, dx\) [477]
3.5.78 \(\int \genfrac {}{}{}{}{1}{(d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^3} \, dx\) [478]
3.5.79 \(\int (d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^{5/2} \, dx\) [479]
3.5.80 \(\int (d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^{3/2} \, dx\) [480]
3.5.81 \(\int \sqrt {d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}}} \, dx\) [481]
3.5.82 \(\int \genfrac {}{}{}{}{1}{\sqrt {d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}}}} \, dx\) [482]
3.5.83 \(\int \genfrac {}{}{}{}{1}{(d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^{3/2}} \, dx\) [483]
3.5.84 \(\int \genfrac {}{}{}{}{1}{(d+e x+f \sqrt {a+b x+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^{5/2}} \, dx\) [484]
3.5.85 \(\int (a+x^2)^2 (x+\sqrt {a+x^2})^n \, dx\) [485]
3.5.86 \(\int (a+x^2) (x+\sqrt {a+x^2})^n \, dx\) [486]
3.5.87 \(\int (x+\sqrt {a+x^2})^n \, dx\) [487]
3.5.88 \(\int \genfrac {}{}{}{}{(x+\sqrt {a+x^2})^n}{a+x^2} \, dx\) [488]
3.5.89 \(\int \genfrac {}{}{}{}{(x+\sqrt {a+x^2})^n}{(a+x^2)^2} \, dx\) [489]
3.5.90 \(\int (a+x^2)^2 (x-\sqrt {a+x^2})^n \, dx\) [490]
3.5.91 \(\int (a+x^2) (x-\sqrt {a+x^2})^n \, dx\) [491]
3.5.92 \(\int (x-\sqrt {a+x^2})^n \, dx\) [492]
3.5.93 \(\int \genfrac {}{}{}{}{(x-\sqrt {a+x^2})^n}{a+x^2} \, dx\) [493]
3.5.94 \(\int \genfrac {}{}{}{}{(x-\sqrt {a+x^2})^n}{(a+x^2)^2} \, dx\) [494]
3.5.95 \(\int (a+x^2)^{5/2} (x+\sqrt {a+x^2})^n \, dx\) [495]
3.5.96 \(\int (a+x^2)^{3/2} (x+\sqrt {a+x^2})^n \, dx\) [496]
3.5.97 \(\int \sqrt {a+x^2} (x+\sqrt {a+x^2})^n \, dx\) [497]
3.5.98 \(\int \genfrac {}{}{}{}{(x+\sqrt {a+x^2})^n}{\sqrt {a+x^2}} \, dx\) [498]
3.5.99 \(\int \genfrac {}{}{}{}{(x+\sqrt {a+x^2})^n}{(a+x^2)^{3/2}} \, dx\) [499]
3.5.100 \(\int \genfrac {}{}{}{}{(x+\sqrt {a+x^2})^n}{(a+x^2)^{5/2}} \, dx\) [500]