3.5.1 \(\int \genfrac {}{}{}{}{\tan (x)}{(-1+\sqrt {\tan (x)})^2} \, dx\) [401]
  3.5.2 \(\int \genfrac {}{}{}{}{\sin (x)}{\sqrt {\sin (2 x)}} \, dx\) [402]
  3.5.3 \(\int \genfrac {}{}{}{}{\cos (x)}{\sqrt {\sin (2 x)}} \, dx\) [403]
  3.5.4 \(\int \sin (x) \sqrt {\sin (2 x)} \, dx\) [404]
  3.5.5 \(\int (\cos (x)-\sin (x)) \sqrt {\sin (2 x)} \, dx\) [405]
  3.5.6 \(\int \genfrac {}{}{}{}{\sin ^7(x)}{\sin ^{\genfrac {}{}{}{}{7}{2}}(2 x)} \, dx\) [406]
  3.5.7 \(\int \genfrac {}{}{}{}{\cos ^7(x)}{\sin ^{\genfrac {}{}{}{}{7}{2}}(2 x)} \, dx\) [407]
  3.5.8 \(\int \csc ^5(x) \sin ^{\genfrac {}{}{}{}{3}{2}}(2 x) \, dx\) [408]
  3.5.9 \(\int \genfrac {}{}{}{}{\sec ^3(x)}{\sqrt {\sin (2 x)}} \, dx\) [409]
  3.5.10 \(\int \genfrac {}{}{}{}{\csc (x)}{\sin ^{\genfrac {}{}{}{}{3}{2}}(2 x)} \, dx\) [410]
  3.5.11 \(\int \genfrac {}{}{}{}{\cos ^3(x) (\cos (2 x)-3 \tan (x))}{(\sin ^2(x)-\sin (2 x)) \sin ^{\genfrac {}{}{}{}{5}{2}}(2 x)} \, dx\) [411]
  3.5.12 \(\int \sqrt {\sec ^4(x) \tan (x)} \, dx\) [412]
  3.5.13 \(\int \sqrt {\sin ^4(x) \tan (x)} \, dx\) [413]
  3.5.14 \(\int \sqrt [3]{\sec ^{12}(x) \tan ^2(x)} \, dx\) [414]
  3.5.15 \(\int \genfrac {}{}{}{}{1}{\sqrt [4]{\cos ^{11}(x) \sin ^{13}(x)}} \, dx\) [415]
  3.5.16 \(\int \genfrac {}{}{}{}{\cos (2 x)-\sqrt {\sin (2 x)}}{\sqrt {\cos ^3(x) \sin (x)}} \, dx\) [416]
  3.5.17 \(\int \genfrac {}{}{}{}{\sqrt {\cos (x) \sin ^3(x)}-2 \sin (2 x)}{-\sqrt {\cos ^3(x) \sin (x)}+\sqrt {\tan (x)}} \, dx\) [417]
  3.5.18 \(\int \genfrac {}{}{}{}{-3 \tan (x)+\sqrt [3]{\sec ^6(x) \tan (x)}}{(\cos ^5(x) \sin (x))^{2/3}} \, dx\) [418]
  3.5.19 \(\int (1+2 \cos ^2(x))^{5/2} \sin (x) \, dx\) [419]
  3.5.20 \(\int \cos (x) (5 \cos ^2(x)+\sin ^2(x))^{5/2} \, dx\) [420]
  3.5.21 \(\int \cos (x) (-\cos ^2(x)-5 \sin ^2(x))^{3/2} \, dx\) [421]
  3.5.22 \(\int \genfrac {}{}{}{}{\sin (x)}{(5 \cos ^2(x)-2 \sin ^2(x))^{7/2}} \, dx\) [422]
  3.5.23 \(\int \genfrac {}{}{}{}{\cos (x) \cos (2 x)}{(2-5 \sin ^2(x))^{3/2}} \, dx\) [423]
  3.5.24 \(\int \genfrac {}{}{}{}{\sin (5 x)}{(5 \cos ^2(x)+9 \sin ^2(x))^{5/2}} \, dx\) [424]
  3.5.25 \(\int \genfrac {}{}{}{}{\cos (x) \cos (2 x) \sin (3 x)}{(-5+4 \sin ^2(x))^{5/2}} \, dx\) [425]
  3.5.26 \(\int \genfrac {}{}{}{}{\csc ^2(x) (-2 \cos ^3(x) (-1+\sin (x))+\cos (2 x) \sin (x))}{\sqrt {-5+\sin ^2(x)}} \, dx\) [426]
  3.5.27 \(\int \genfrac {}{}{}{}{\cos (3 x)}{-\sqrt {-1+8 \cos ^2(x)}+\sqrt {3 \cos ^2(x)-\sin ^2(x)}} \, dx\) [427]
  3.5.28 \(\int (2-3 \sin ^2(x))^{3/5} \sin (4 x) \, dx\) [428]
  3.5.29 \(\int \cos (x) \sqrt {\cos (2 x)} \, dx\) [429]
  3.5.30 \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(2 x) \sin (x) \, dx\) [430]
  3.5.31 \(\int \genfrac {}{}{}{}{\sin (x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(2 x)} \, dx\) [431]
  3.5.32 \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(2 x) \sec ^3(x) \, dx\) [432]
  3.5.33 \(\int \genfrac {}{}{}{}{\sin ^2(x) (3 \sin ^3(x)-\cos (x) \sin (4 x))}{\cos ^{\genfrac {}{}{}{}{7}{2}}(2 x)} \, dx\) [433]
  3.5.34 \(\int (4-5 \sec ^2(x))^{3/2} \, dx\) [434]
  3.5.35 \(\int \genfrac {}{}{}{}{1}{(4-5 \sec ^2(x))^{3/2}} \, dx\) [435]
  3.5.36 \(\int \genfrac {}{}{}{}{-2 \cot ^2(x)+\sin (x)}{(1+5 \tan ^2(x))^{3/2}} \, dx\) [436]
  3.5.37 \(\int \genfrac {}{}{}{}{(-3+\cos (2 x)) \sec ^4(x)}{\sqrt {4-\cot ^2(x)}} \, dx\) [437]
  3.5.38 \(\int \genfrac {}{}{}{}{(3+\sin ^2(x)) \tan ^3(x)}{(-2+\cos ^2(x)) (5-4 \sec ^2(x))^{3/2}} \, dx\) [438]
  3.5.39 \(\int \genfrac {}{}{}{}{\csc ^2(x) (\sec ^2(x)-3 \tan (x) \sqrt {4 \sec ^2(x)+5 \tan ^2(x)})}{(4 \sec ^2(x)+5 \tan ^2(x))^{3/2}} \, dx\) [439]
  3.5.40 \(\int \tan (x) (1+5 \tan ^2(x))^{5/2} \, dx\) [440]
  3.5.41 \(\int \genfrac {}{}{}{}{\tan (x)}{(1+5 \tan ^2(x))^{5/2}} \, dx\) [441]
  3.5.42 \(\int \genfrac {}{}{}{}{\tan (x)}{\sqrt [3]{a^3+b^3 \tan ^2(x)}} \, dx\) [442]
  3.5.43 \(\int \tan (x) (1-7 \tan ^2(x))^{2/3} \, dx\) [443]
  3.5.44 \(\int \genfrac {}{}{}{}{\cot (x)}{\sqrt [4]{a^4+b^4 \csc ^2(x)}} \, dx\) [444]
  3.5.45 \(\int \genfrac {}{}{}{}{\cot (x)}{\sqrt [4]{a^4-b^4 \csc ^2(x)}} \, dx\) [445]
  3.5.46 \(\int \genfrac {}{}{}{}{\sec ^2(x) \tan (x) (\sqrt [3]{1-3 \sec ^2(x)} \sin ^2(x)+3 \tan ^2(x))}{(1-3 \sec ^2(x))^{5/6} (1-\sqrt {1-3 \sec ^2(x)})} \, dx\) [446]
  3.5.47 \(\int \genfrac {}{}{}{}{\sec ^2(x) (-\cos (2 x)+2 \tan ^2(x))}{(\tan (x) \tan (2 x))^{3/2}} \, dx\) [447]
  3.5.48 \(\int \genfrac {}{}{}{}{\tan (x)}{(a^3-b^3 \cos ^n(x))^{4/3}} \, dx\) [448]
  3.5.49 \(\int (1+2 \cos ^9(x))^{5/6} \tan (x) \, dx\) [449]
  3.5.50 \(\int \genfrac {}{}{}{}{\cos (x) \sin ^8(x)}{(2-5 \sin ^3(x))^{4/3}} \, dx\) [450]
  3.5.51 \(\int \genfrac {}{}{}{}{\sec ^2(x) \tan (x) (1+\sqrt [3]{1-8 \tan ^2(x)})}{(1-8 \tan ^2(x))^{2/3}} \, dx\) [451]
  3.5.52 \(\int \genfrac {}{}{}{}{\csc (x) \sec (x) (1+\sqrt [3]{1-8 \tan ^2(x)})}{(1-8 \tan ^2(x))^{2/3}} \, dx\) [452]
  3.5.53 \(\int \genfrac {}{}{}{}{(5 \cos ^2(x)-\sqrt {-1+5 \sin ^2(x)}) \tan (x)}{\sqrt [4]{-1+5 \sin ^2(x)} (2+\sqrt {-1+5 \sin ^2(x)})} \, dx\) [453]
  3.5.54 \(\int \cos ^3(x) \cos ^{\genfrac {}{}{}{}{2}{3}}(2 x) \sin (x) \, dx\) [454]
  3.5.55 \(\int \genfrac {}{}{}{}{\sin ^6(x) \tan (x)}{\cos ^{\genfrac {}{}{}{}{3}{4}}(2 x)} \, dx\) [455]
  3.5.56 \(\int \sqrt {\tan (x) \tan (2 x)} \, dx\) [456]
  3.5.57 \(\int \sqrt {\cot (2 x) \tan (x)} \, dx\) [457]
  3.5.58 \(\int \genfrac {}{}{}{}{1}{x^5 (5+x^2)} \, dx\) [458]
  3.5.59 \(\int \genfrac {}{}{}{}{1}{x^6 (5+x^2)} \, dx\) [459]
  3.5.60 \(\int \genfrac {}{}{}{}{1}{x (-4+x^2)^4} \, dx\) [460]
  3.5.61 \(\int \genfrac {}{}{}{}{1}{x (-2+x^2)^{5/2}} \, dx\) [461]
  3.5.62 \(\int \genfrac {}{}{}{}{(-10+x^2)^{5/2}}{x} \, dx\) [462]
  3.5.63 \(\int x^{1+2 n} \, dx\) [463]
  3.5.64 \(\int \genfrac {}{}{}{}{x^7}{(-5+x^2)^3} \, dx\) [464]
  3.5.65 \(\int \genfrac {}{}{}{}{-4 x^3+3 x^5}{(-1+x^2)^5} \, dx\) [465]
  3.5.66 \(\int x^3 (1+x^2)^{9/14} \, dx\) [466]
  3.5.67 \(\int \genfrac {}{}{}{}{x^5}{(-4+x^2)^{13/6}} \, dx\) [467]
  3.5.68 \(\int \genfrac {}{}{}{}{1}{(1+2 x^2)^{5/2}} \, dx\) [468]
  3.5.69 \(\int \genfrac {}{}{}{}{1}{(-1-2 x+x^2)^{5/2}} \, dx\) [469]
  3.5.70 \(\int \genfrac {}{}{}{}{1}{x^4 (-8+x^2)^{3/2}} \, dx\) [470]
  3.5.71 \(\int \genfrac {}{}{}{}{(5+x^2)^2}{x^{13/3}} \, dx\) [471]
  3.5.72 \(\int \genfrac {}{}{}{}{1}{x^7 (1+x^2)^3} \, dx\) [472]
  3.5.73 \(\int \genfrac {}{}{}{}{(\genfrac {}{}{}{}{2+x^2}{x^2})^{7/9}}{(2+x^2)^{3/2}} \, dx\) [473]
  3.5.74 \(\int \genfrac {}{}{}{}{x^4}{(\sqrt {10}-x^2)^{9/2}} \, dx\) [474]
  3.5.75 \(\int \genfrac {}{}{}{}{x^2}{(3-x^2)^{3/2}} \, dx\) [475]
  3.5.76 \(\int \genfrac {}{}{}{}{(25-x^2)^{3/2}}{x^4} \, dx\) [476]
  3.5.77 \(\int \genfrac {}{}{}{}{1}{(1-2 x^2)^{7/2}} \, dx\) [477]
  3.5.78 \(\int \genfrac {}{}{}{}{1}{(-7+6 x-x^2)^{5/2}} \, dx\) [478]
  3.5.79 \(\int (1-2 x-2 x^2)^3 \, dx\) [479]
  3.5.80 \(\int (-1+5 x) (-1-x+x^2)^2 \, dx\) [480]
  3.5.81 \(\int \genfrac {}{}{}{}{1+3 x}{(1-8 x+2 x^2)^{5/2}} \, dx\) [481]
  3.5.82 \(\int \genfrac {}{}{}{}{-1-8 x+8 x^3}{(1+2 x-4 x^2)^{5/2}} \, dx\) [482]
  3.5.83 \(\int x^2 \cos ^5(x) \, dx\) [483]
  3.5.84 \(\int x^3 \sin ^3(x) \, dx\) [484]
  3.5.85 \(\int x^2 \sin ^6(x) \, dx\) [485]
  3.5.86 \(\int x^2 \cos (x) \sin ^2(x) \, dx\) [486]
  3.5.87 \(\int x \cos ^2(x) \cot ^2(x) \, dx\) [487]
  3.5.88 \(\int x \sec (x) \tan ^3(x) \, dx\) [488]
  3.5.89 \(\int x \sec ^2(x) \tan (x) \, dx\) [489]
  3.5.90 \(\int x \sin ^2(x) \tan (x) \, dx\) [490]
  3.5.91 \(\int x \tan ^3(x) \, dx\) [491]
  3.5.92 \(\int \genfrac {}{}{}{}{2 x+\sin (2 x)}{(\cos (x)+x \sin (x))^2} \, dx\) [492]
  3.5.93 \(\int \genfrac {}{}{}{}{x^2}{(x \cos (x)-\sin (x))^2} \, dx\) [493]
  3.5.94 \(\int a^{m x} b^{n x} \, dx\) [494]
  3.5.95 \(\int a^{-x} b^{-x} (a^x-b^x)^2 \, dx\) [495]
  3.5.96 \(\int (-e^{-x}+e^x) \, dx\) [496]
  3.5.97 \(\int (-e^{-x}+e^x)^2 \, dx\) [497]
  3.5.98 \(\int (-e^{-x}+e^x)^3 \, dx\) [498]
  3.5.99 \(\int (-e^{-x}+e^x)^4 \, dx\) [499]
  3.5.100 \(\int (-e^{-x}+e^x)^n \, dx\) [500]