3.6 Integrals 501 to 569

  3.6.1 \(\int \genfrac {}{}{}{}{a+b \cosh ^{-1}(c x)}{x^3 (d+e x^2)^2} \, dx\) [501]
  3.6.2 \(\int \genfrac {}{}{}{}{x^4 (a+b \cosh ^{-1}(c x))}{(d+e x^2)^2} \, dx\) [502]
  3.6.3 \(\int \genfrac {}{}{}{}{x^2 (a+b \cosh ^{-1}(c x))}{(d+e x^2)^2} \, dx\) [503]
  3.6.4 \(\int \genfrac {}{}{}{}{a+b \cosh ^{-1}(c x)}{(d+e x^2)^2} \, dx\) [504]
  3.6.5 \(\int \genfrac {}{}{}{}{a+b \cosh ^{-1}(c x)}{x^2 (d+e x^2)^2} \, dx\) [505]
  3.6.6 \(\int \genfrac {}{}{}{}{x^5 (a+b \cosh ^{-1}(c x))}{(d+e x^2)^3} \, dx\) [506]
  3.6.7 \(\int \genfrac {}{}{}{}{x^3 (a+b \cosh ^{-1}(c x))}{(d+e x^2)^3} \, dx\) [507]
  3.6.8 \(\int \genfrac {}{}{}{}{x (a+b \cosh ^{-1}(c x))}{(d+e x^2)^3} \, dx\) [508]
  3.6.9 \(\int \genfrac {}{}{}{}{a+b \cosh ^{-1}(c x)}{x (d+e x^2)^3} \, dx\) [509]
  3.6.10 \(\int \genfrac {}{}{}{}{a+b \cosh ^{-1}(c x)}{x^3 (d+e x^2)^3} \, dx\) [510]
  3.6.11 \(\int \genfrac {}{}{}{}{x^4 (a+b \cosh ^{-1}(c x))}{(d+e x^2)^3} \, dx\) [511]
  3.6.12 \(\int \genfrac {}{}{}{}{x^2 (a+b \cosh ^{-1}(c x))}{(d+e x^2)^3} \, dx\) [512]
  3.6.13 \(\int \genfrac {}{}{}{}{a+b \cosh ^{-1}(c x)}{(d+e x^2)^3} \, dx\) [513]
  3.6.14 \(\int \sqrt {d+e x^2} (a+b \cosh ^{-1}(c x)) \, dx\) [514]
  3.6.15 \(\int \genfrac {}{}{}{}{a+b \cosh ^{-1}(c x)}{\sqrt {d+e x^2}} \, dx\) [515]
  3.6.16 \(\int \genfrac {}{}{}{}{a+b \cosh ^{-1}(c x)}{(d+e x^2)^{3/2}} \, dx\) [516]
  3.6.17 \(\int \genfrac {}{}{}{}{a+b \cosh ^{-1}(c x)}{(d+e x^2)^{5/2}} \, dx\) [517]
  3.6.18 \(\int \genfrac {}{}{}{}{a+b \cosh ^{-1}(c x)}{(d+e x^2)^{7/2}} \, dx\) [518]
  3.6.19 \(\int (f x)^m (d+e x^2)^3 (a+b \cosh ^{-1}(c x)) \, dx\) [519]
  3.6.20 \(\int (f x)^m (d+e x^2)^2 (a+b \cosh ^{-1}(c x)) \, dx\) [520]
  3.6.21 \(\int (f x)^m (d+e x^2) (a+b \cosh ^{-1}(c x)) \, dx\) [521]
  3.6.22 \(\int \genfrac {}{}{}{}{(f x)^m (a+b \cosh ^{-1}(c x))}{d+e x^2} \, dx\) [522]
  3.6.23 \(\int \genfrac {}{}{}{}{(f x)^m (a+b \cosh ^{-1}(c x))}{(d+e x^2)^2} \, dx\) [523]
  3.6.24 \(\int \genfrac {}{}{}{}{(f x)^m (a+b \cosh ^{-1}(c x))}{(d+e x^2)^3} \, dx\) [524]
  3.6.25 \(\int (d+e x^2)^3 (a+b \cosh ^{-1}(c x))^2 \, dx\) [525]
  3.6.26 \(\int (d+e x^2)^2 (a+b \cosh ^{-1}(c x))^2 \, dx\) [526]
  3.6.27 \(\int (d+e x^2) (a+b \cosh ^{-1}(c x))^2 \, dx\) [527]
  3.6.28 \(\int (a+b \cosh ^{-1}(c x))^2 \, dx\) [528]
  3.6.29 \(\int \genfrac {}{}{}{}{(a+b \cosh ^{-1}(c x))^2}{d+e x^2} \, dx\) [529]
  3.6.30 \(\int \sqrt {d+e x^2} (a+b \cosh ^{-1}(c x))^2 \, dx\) [530]
  3.6.31 \(\int \genfrac {}{}{}{}{(a+b \cosh ^{-1}(c x))^2}{\sqrt {d+e x^2}} \, dx\) [531]
  3.6.32 \(\int \genfrac {}{}{}{}{(a+b \cosh ^{-1}(c x))^2}{(d+e x^2)^{3/2}} \, dx\) [532]
  3.6.33 \(\int \genfrac {}{}{}{}{(a+b \cosh ^{-1}(c x))^2}{(d+e x^2)^{5/2}} \, dx\) [533]
  3.6.34 \(\int \genfrac {}{}{}{}{(d+e x^2)^2}{a+b \cosh ^{-1}(c x)} \, dx\) [534]
  3.6.35 \(\int \genfrac {}{}{}{}{d+e x^2}{a+b \cosh ^{-1}(c x)} \, dx\) [535]
  3.6.36 \(\int \genfrac {}{}{}{}{1}{a+b \cosh ^{-1}(c x)} \, dx\) [536]
  3.6.37 \(\int \genfrac {}{}{}{}{1}{(d+e x^2) (a+b \cosh ^{-1}(c x))} \, dx\) [537]
  3.6.38 \(\int \genfrac {}{}{}{}{1}{(d+e x^2)^2 (a+b \cosh ^{-1}(c x))} \, dx\) [538]
  3.6.39 \(\int \genfrac {}{}{}{}{\sqrt {d+e x^2}}{a+b \cosh ^{-1}(c x)} \, dx\) [539]
  3.6.40 \(\int \genfrac {}{}{}{}{1}{\sqrt {d+e x^2} (a+b \cosh ^{-1}(c x))} \, dx\) [540]
  3.6.41 \(\int \genfrac {}{}{}{}{1}{(d+e x^2)^{3/2} (a+b \cosh ^{-1}(c x))} \, dx\) [541]
  3.6.42 \(\int \genfrac {}{}{}{}{1}{(d+e x^2)^{5/2} (a+b \cosh ^{-1}(c x))} \, dx\) [542]
  3.6.43 \(\int \genfrac {}{}{}{}{(d+e x^2)^2}{(a+b \cosh ^{-1}(c x))^2} \, dx\) [543]
  3.6.44 \(\int \genfrac {}{}{}{}{d+e x^2}{(a+b \cosh ^{-1}(c x))^2} \, dx\) [544]
  3.6.45 \(\int \genfrac {}{}{}{}{1}{(a+b \cosh ^{-1}(c x))^2} \, dx\) [545]
  3.6.46 \(\int \genfrac {}{}{}{}{1}{(d+e x^2) (a+b \cosh ^{-1}(c x))^2} \, dx\) [546]
  3.6.47 \(\int \genfrac {}{}{}{}{1}{(d+e x^2)^2 (a+b \cosh ^{-1}(c x))^2} \, dx\) [547]
  3.6.48 \(\int \genfrac {}{}{}{}{\sqrt {d+e x^2}}{(a+b \cosh ^{-1}(c x))^2} \, dx\) [548]
  3.6.49 \(\int \genfrac {}{}{}{}{1}{\sqrt {d+e x^2} (a+b \cosh ^{-1}(c x))^2} \, dx\) [549]
  3.6.50 \(\int \genfrac {}{}{}{}{1}{(d+e x^2)^{3/2} (a+b \cosh ^{-1}(c x))^2} \, dx\) [550]
  3.6.51 \(\int \genfrac {}{}{}{}{1}{(d+e x^2)^{5/2} (a+b \cosh ^{-1}(c x))^2} \, dx\) [551]
  3.6.52 \(\int (d+e x^2)^2 \sqrt {a+b \cosh ^{-1}(c x)} \, dx\) [552]
  3.6.53 \(\int (d+e x^2) \sqrt {a+b \cosh ^{-1}(c x)} \, dx\) [553]
  3.6.54 \(\int \sqrt {a+b \cosh ^{-1}(c x)} \, dx\) [554]
  3.6.55 \(\int \genfrac {}{}{}{}{\sqrt {a+b \cosh ^{-1}(c x)}}{d+e x^2} \, dx\) [555]
  3.6.56 \(\int \genfrac {}{}{}{}{\sqrt {a+b \cosh ^{-1}(c x)}}{(d+e x^2)^2} \, dx\) [556]
  3.6.57 \(\int (d+e x^2) (a+b \cosh ^{-1}(c x))^{3/2} \, dx\) [557]
  3.6.58 \(\int (a+b \cosh ^{-1}(c x))^{3/2} \, dx\) [558]
  3.6.59 \(\int \genfrac {}{}{}{}{(a+b \cosh ^{-1}(c x))^{3/2}}{d+e x^2} \, dx\) [559]
  3.6.60 \(\int \genfrac {}{}{}{}{(a+b \cosh ^{-1}(c x))^{3/2}}{(d+e x^2)^2} \, dx\) [560]
  3.6.61 \(\int \genfrac {}{}{}{}{(d+e x^2)^2}{\sqrt {a+b \cosh ^{-1}(c x)}} \, dx\) [561]
  3.6.62 \(\int \genfrac {}{}{}{}{d+e x^2}{\sqrt {a+b \cosh ^{-1}(c x)}} \, dx\) [562]
  3.6.63 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \cosh ^{-1}(c x)}} \, dx\) [563]
  3.6.64 \(\int \genfrac {}{}{}{}{1}{(d+e x^2) \sqrt {a+b \cosh ^{-1}(c x)}} \, dx\) [564]
  3.6.65 \(\int \genfrac {}{}{}{}{1}{(d+e x^2)^2 \sqrt {a+b \cosh ^{-1}(c x)}} \, dx\) [565]
  3.6.66 \(\int \genfrac {}{}{}{}{d+e x^2}{(a+b \cosh ^{-1}(c x))^{3/2}} \, dx\) [566]
  3.6.67 \(\int \genfrac {}{}{}{}{1}{(a+b \cosh ^{-1}(c x))^{3/2}} \, dx\) [567]
  3.6.68 \(\int \genfrac {}{}{}{}{1}{(d+e x^2) (a+b \cosh ^{-1}(c x))^{3/2}} \, dx\) [568]
  3.6.69 \(\int \genfrac {}{}{}{}{1}{(d+e x^2)^2 (a+b \cosh ^{-1}(c x))^{3/2}} \, dx\) [569]