3.6 Integrals 501 to 600

  3.6.1 \(\int (a^{-4 x}-a^{2 x})^3 \, dx\) [501]
  3.6.2 \(\int (a^{k x}+a^{l x}) \, dx\) [502]
  3.6.3 \(\int (a^{k x}+a^{l x})^2 \, dx\) [503]
  3.6.4 \(\int (a^{k x}+a^{l x})^3 \, dx\) [504]
  3.6.5 \(\int (a^{k x}+a^{l x})^4 \, dx\) [505]
  3.6.6 \(\int (a^{k x}+a^{l x})^n \, dx\) [506]
  3.6.7 \(\int (a^{k x}-a^{l x}) \, dx\) [507]
  3.6.8 \(\int (a^{k x}-a^{l x})^2 \, dx\) [508]
  3.6.9 \(\int (a^{k x}-a^{l x})^3 \, dx\) [509]
  3.6.10 \(\int (a^{k x}-a^{l x})^4 \, dx\) [510]
  3.6.11 \(\int (a^{k x}-a^{l x})^n \, dx\) [511]
  3.6.12 \(\int (1+a^{m x}) \, dx\) [512]
  3.6.13 \(\int (1+a^{m x})^2 \, dx\) [513]
  3.6.14 \(\int (1+a^{m x})^3 \, dx\) [514]
  3.6.15 \(\int (1+a^{m x})^4 \, dx\) [515]
  3.6.16 \(\int (1+a^{m x})^n \, dx\) [516]
  3.6.17 \(\int (1-a^{m x}) \, dx\) [517]
  3.6.18 \(\int (1-a^{m x})^2 \, dx\) [518]
  3.6.19 \(\int (1-a^{m x})^3 \, dx\) [519]
  3.6.20 \(\int (1-a^{m x})^4 \, dx\) [520]
  3.6.21 \(\int (1-a^{m x})^n \, dx\) [521]
  3.6.22 \(\int \genfrac {}{}{}{}{1}{b+a e^{n x}} \, dx\) [522]
  3.6.23 \(\int \genfrac {}{}{}{}{e^x}{b+a e^{3 x}} \, dx\) [523]
  3.6.24 \(\int \genfrac {}{}{}{}{-1+e^x}{1+e^x} \, dx\) [524]
  3.6.25 \(\int \genfrac {}{}{}{}{e^{4 x}}{1-2 e^{2 x}+3 e^{4 x}} \, dx\) [525]
  3.6.26 \(\int \genfrac {}{}{}{}{e^x+e^{5 x}}{-1+e^x-e^{2 x}+e^{3 x}} \, dx\) [526]
  3.6.27 \(\int e^{n x} (a+b e^{n x})^{r/s} \, dx\) [527]
  3.6.28 \(\int \sqrt [4]{1-2 e^{x/3}} \, dx\) [528]
  3.6.29 \(\int (a+b e^{n x})^{r/s} \, dx\) [529]
  3.6.30 \(\int \genfrac {}{}{}{}{e^x}{\sqrt {a^2+e^{2 x}}} \, dx\) [530]
  3.6.31 \(\int \genfrac {}{}{}{}{e^x}{\sqrt {-a^2+e^{2 x}}} \, dx\) [531]
  3.6.32 \(\int \genfrac {}{}{}{}{e^{3 x/4}}{(-2+e^{3 x/4}) \sqrt {-2+e^{3 x/4}+e^{3 x/2}}} \, dx\) [532]
  3.6.33 \(\int e^{-2 x} (-3+e^{7 x})^{2/3} \, dx\) [533]
  3.6.34 \(\int \genfrac {}{}{}{}{e^{2 x}}{(3-e^{x/2})^{3/4}} \, dx\) [534]
  3.6.35 \(\int e^{-x/2} x^3 \, dx\) [535]
  3.6.36 \(\int \genfrac {}{}{}{}{e^{-x/2}}{x^3} \, dx\) [536]
  3.6.37 \(\int a^{3 x} x^2 \, dx\) [537]
  3.6.38 \(\int e^{x^2} x (1+x^2) \, dx\) [538]
  3.6.39 \(\int \genfrac {}{}{}{}{x}{(e^{-x}+e^x)^2} \, dx\) [539]
  3.6.40 \(\int \genfrac {}{}{}{}{e^x (1-x-x^2)}{\sqrt {1-x^2}} \, dx\) [540]
  3.6.41 \(\int e^{-3 x} \cos (2 x) \, dx\) [541]
  3.6.42 \(\int \genfrac {}{}{}{}{\cos (\genfrac {}{}{}{}{x}{2})+\sin (\genfrac {}{}{}{}{x}{2})}{\sqrt [3]{e^x}} \, dx\) [542]
  3.6.43 \(\int \genfrac {}{}{}{}{\cos (\genfrac {}{}{}{}{3 x}{2})}{\sqrt [4]{3^{3 x}}} \, dx\) [543]
  3.6.44 \(\int e^{m x} \cos ^2(x) \, dx\) [544]
  3.6.45 \(\int e^{m x} \sin ^3(x) \, dx\) [545]
  3.6.46 \(\int \genfrac {}{}{}{}{\cos ^3(\genfrac {}{}{}{}{x}{3})}{\sqrt {e^x}} \, dx\) [546]
  3.6.47 \(\int e^{2 x} \cos ^2(x) \sin ^2(x) \, dx\) [547]
  3.6.48 \(\int e^{3 x} \cos ^2(\genfrac {}{}{}{}{3 x}{2}) \sin ^2(\genfrac {}{}{}{}{3 x}{2}) \, dx\) [548]
  3.6.49 \(\int e^{m x} \tan ^2(x) \, dx\) [549]
  3.6.50 \(\int e^{m x} \csc ^2(x) \, dx\) [550]
  3.6.51 \(\int e^{m x} \sec ^3(x) \, dx\) [551]
  3.6.52 \(\int \genfrac {}{}{}{}{e^x}{1+\cos (x)} \, dx\) [552]
  3.6.53 \(\int \genfrac {}{}{}{}{e^x}{1-\cos (x)} \, dx\) [553]
  3.6.54 \(\int \genfrac {}{}{}{}{e^x}{1+\sin (x)} \, dx\) [554]
  3.6.55 \(\int \genfrac {}{}{}{}{e^x}{1-\sin (x)} \, dx\) [555]
  3.6.56 \(\int \genfrac {}{}{}{}{e^x (1-\sin (x))}{1-\cos (x)} \, dx\) [556]
  3.6.57 \(\int \genfrac {}{}{}{}{e^x (1+\sin (x))}{1-\cos (x)} \, dx\) [557]
  3.6.58 \(\int \genfrac {}{}{}{}{e^x (1+\sin (x))}{1+\cos (x)} \, dx\) [558]
  3.6.59 \(\int \genfrac {}{}{}{}{e^x (1-\sin (x))}{1+\cos (x)} \, dx\) [559]
  3.6.60 \(\int \genfrac {}{}{}{}{e^x (1-\cos (x))}{1-\sin (x)} \, dx\) [560]
  3.6.61 \(\int \genfrac {}{}{}{}{e^x (1+\cos (x))}{1-\sin (x)} \, dx\) [561]
  3.6.62 \(\int \genfrac {}{}{}{}{e^x (1+\cos (x))}{1+\sin (x)} \, dx\) [562]
  3.6.63 \(\int \genfrac {}{}{}{}{e^x (1-\cos (x))}{1+\sin (x)} \, dx\) [563]
  3.6.64 \(\int e^x x \cos (x) \, dx\) [564]
  3.6.65 \(\int e^x x^2 \sin (x) \, dx\) [565]
  3.6.66 \(\int e^{-3 x} x^2 \sin (x) \, dx\) [566]
  3.6.67 \(\int e^{x/2} x^2 \cos ^3(x) \, dx\) [567]
  3.6.68 \(\int e^{2 x} x^2 \sin (4 x) \, dx\) [568]
  3.6.69 \(\int e^{x/2} x^2 \cos (x) \sin ^2(x) \, dx\) [569]
  3.6.70 \(\int \cosh (x) \, dx\) [570]
  3.6.71 \(\int \sinh (x) \, dx\) [571]
  3.6.72 \(\int \tanh (x) \, dx\) [572]
  3.6.73 \(\int \coth (x) \, dx\) [573]
  3.6.74 \(\int \text {sech}(x) \, dx\) [574]
  3.6.75 \(\int \text {csch}(x) \, dx\) [575]
  3.6.76 \(\int \cosh ^2(x) \, dx\) [576]
  3.6.77 \(\int \sinh ^5(x) \, dx\) [577]
  3.6.78 \(\int \tanh ^4(x) \, dx\) [578]
  3.6.79 \(\int \text {csch}^3(x) \, dx\) [579]
  3.6.80 \(\int \text {sech}^5(x) \, dx\) [580]
  3.6.81 \(\int \sinh ^4(x) \tanh (x) \, dx\) [581]
  3.6.82 \(\int \text {sech}^{\genfrac {}{}{}{}{23}{4}}(x) \sinh ^5(x) \, dx\) [582]
  3.6.83 \(\int \genfrac {}{}{}{}{1}{a+b \cosh (x)} \, dx\) [583]
  3.6.84 \(\int \genfrac {}{}{}{}{1}{(1+\cosh (x))^2} \, dx\) [584]
  3.6.85 \(\int \genfrac {}{}{}{}{1}{a+b \tanh (x)} \, dx\) [585]
  3.6.86 \(\int \genfrac {}{}{}{}{1}{a^2+b^2 \cosh ^2(x)} \, dx\) [586]
  3.6.87 \(\int \genfrac {}{}{}{}{1}{a^2-b^2 \cosh ^2(x)} \, dx\) [587]
  3.6.88 \(\int \genfrac {}{}{}{}{1}{1-\sinh ^4(x)} \, dx\) [588]
  3.6.89 \(\int \genfrac {}{}{}{}{\cosh ^3(x)-\sinh ^3(x)}{\cosh ^3(x)+\sinh ^3(x)} \, dx\) [589]
  3.6.90 \(\int \cosh (x) \cosh (2 x) \cosh (3 x) \, dx\) [590]
  3.6.91 \(\int \cosh (\genfrac {}{}{}{}{3 x}{2}) \sinh (x) \sinh (\genfrac {}{}{}{}{5 x}{2}) \, dx\) [591]
  3.6.92 \(\int \genfrac {}{}{}{}{\cosh (x) (-\cosh (2 x)+\tanh (x))}{\sqrt {\sinh (2 x)} (\sinh ^2(x)+\sinh (2 x))} \, dx\) [592]
  3.6.93 \(\int \genfrac {}{}{}{}{\sinh (x)}{(-9+4 \cosh ^2(x))^{5/2}} \, dx\) [593]
  3.6.94 \(\int \genfrac {}{}{}{}{\sinh ^2(x) \sinh (2 x)}{(1-\sinh ^2(x))^{3/2}} \, dx\) [594]
  3.6.95 \(\int \genfrac {}{}{}{}{\cosh (x)}{\sqrt {\cosh (2 x)}} \, dx\) [595]
  3.6.96 \(\int x \tanh ^2(x) \, dx\) [596]
  3.6.97 \(\int x \coth ^2(x) \, dx\) [597]
  3.6.98 \(\int \genfrac {}{}{}{}{x+\cosh (x)+\sinh (x)}{\cosh (x)-\sinh (x)} \, dx\) [598]
  3.6.99 \(\int \genfrac {}{}{}{}{x+\cosh (x)+\sinh (x)}{1+\cosh (x)} \, dx\) [599]
  3.6.100 \(\int e^{2 x} \text {csch}^4(x) \, dx\) [600]