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sech^2(x)tanh^5(x)
Solving integrals/ sech^2(x)tanh^5(x)

Integral of sech^2(x)tanh^5(x) dx

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The solution

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  3                     
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 |      2        5      
 |  sech (x)*tanh (x) dx
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2
∫23tanh⁡5(x)sech⁡2(x) dx\int\limits_{2}^{3} \tanh^{5}{\left(x \right)} \operatorname{sech}^{2}{\left(x \right)}\, dx 
Integral(sech(x)^2*tanh(x)^5, (x, 2, 3))
The answer (Indefinite) [src] 
  /                                                                           
 |                                2          2        2          2        4   
 |     2        5             sech (x)   sech (x)*tanh (x)   sech (x)*tanh (x)
 | sech (x)*tanh (x) dx = C - -------- - ----------------- - -----------------
 |                               6               6                   6        
/
tanh⁡6x6{{\tanh ^6x}\over{6}}
Simplify
The graph
2.003.002.102.202.302.402.502.602.702.802.900.1-0.1
Plot the graph f(x)
The answer [src] 
      2          2          2        2          2        4          2        2          2        4   
  sech (3)   sech (2)   sech (3)*tanh (3)   sech (3)*tanh (3)   sech (2)*tanh (2)   sech (2)*tanh (2)
- -------- + -------- - ----------------- - ----------------- + ----------------- + -----------------
     6          6               6                   6                   6                   6
6 e20+20 e12+6 e43 e24+18 e20+45 e16+60 e12+45 e8+18 e4+3−6 e30+20 e18+6 e63 e36+18 e30+45 e24+60 e18+45 e12+18 e6+3{{6\,e^{20}+20\,e^{12}+6\,e^4}\over{3\,e^{24}+18\,e^{20}+45\,e^{16} +60\,e^{12}+45\,e^8+18\,e^4+3}}-{{6\,e^{30}+20\,e^{18}+6\,e^6}\over{ 3\,e^{36}+18\,e^{30}+45\,e^{24}+60\,e^{18}+45\,e^{12}+18\,e^6+3}} 
=
= 
      2          2          2        2          2        4          2        2          2        4   
  sech (3)   sech (2)   sech (3)*tanh (3)   sech (3)*tanh (3)   sech (2)*tanh (2)   sech (2)*tanh (2)
- -------- + -------- - ----------------- - ----------------- + ----------------- + -----------------
     6          6               6                   6                   6                   6
−sech⁡2(3)6−tanh⁡2(3)sech⁡2(3)6−tanh⁡4(3)sech⁡2(3)6+tanh⁡4(2)sech⁡2(2)6+tanh⁡2(2)sech⁡2(2)6+sech⁡2(2)6- \frac{\operatorname{sech}^{2}{\left(3 \right)}}{6} - \frac{\tanh^{2}{\left(3 \right)} \operatorname{sech}^{2}{\left(3 \right)}}{6} - \frac{\tanh^{4}{\left(3 \right)} \operatorname{sech}^{2}{\left(3 \right)}}{6} + \frac{\tanh^{4}{\left(2 \right)} \operatorname{sech}^{2}{\left(2 \right)}}{6} + \frac{\tanh^{2}{\left(2 \right)} \operatorname{sech}^{2}{\left(2 \right)}}{6} + \frac{\operatorname{sech}^{2}{\left(2 \right)}}{6}
Simplify
Numerical answer [src] 
0.0280039096630232
0.0280039096630232
The graph
Integral of sech^2(x)tanh^5(x) dx

    Use the examples entering the upper and lower limits of integration.

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