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x/(1+cos(x))
Solving integrals/ x/(1+cos(x))

Integral of x/(1+cos(x)) dx

Limits of integration:

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The solution

You have entered [src] 
  1              
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 |      x        
 |  ---------- dx
 |  1 + cos(x)   
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0
∫01xcos⁡(x)+1 dx\int\limits_{0}^{1} \frac{x}{\cos{\left(x \right)} + 1}\, dx 
Integral(x/(1 + cos(x)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                               
 |                                                
 |     x                  /       2/x\\        /x\
 | ---------- dx = C - log|1 + tan |-|| + x*tan|-|
 | 1 + cos(x)             \        \2//        \2/
 |                                                
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(sin⁡2x+cos⁡2x+2 cos⁡x+1) log⁡(sin⁡2x+cos⁡2x+2 cos⁡x+1)+2 x sin⁡xsin⁡2x+cos⁡2x+2 cos⁡x+1{{\left(\sin ^2x+\cos ^2x+2\,\cos x+1\right)\,\log \left(\sin ^2x+ \cos ^2x+2\,\cos x+1\right)+2\,x\,\sin x}\over{\sin ^2x+\cos ^2x+2\, \cos x+1}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Plot the graph f(x)
The answer [src] 
     /       2     \           
- log\1 + tan (1/2)/ + tan(1/2)
(sin⁡21+cos⁡21+2 cos⁡1+1) log⁡(sin⁡21+cos⁡21+2 cos⁡1+1)+2 sin⁡1sin⁡21+cos⁡21+2 cos⁡1+1−2 log⁡2{{\left(\sin ^21+\cos ^21+2\,\cos 1+1\right)\,\log \left(\sin ^21+ \cos ^21+2\,\cos 1+1\right)+2\,\sin 1}\over{\sin ^21+\cos ^21+2\, \cos 1+1}}-2\,\log 2 
=
= 
     /       2     \           
- log\1 + tan (1/2)/ + tan(1/2)
−log⁡(tan⁡2(12)+1)+tan⁡(12)- \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} + \tan{\left(\frac{1}{2} \right)}
Упростить
Numerical answer [src] 
0.285134008956345
0.285134008956345
The graph
Integral of x/(1+cos(x)) dx

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

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