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∫(x+sinx)/(1+cosx)dx

∫(x+sinx)/(1+cosx)dx

Grade:12

2 Answers

Vikas TU
14149 Points
7 years ago
 
∫(x+sinx)/(1+cosx)dx
 
 => write sinx and cosx in half angle formulaes:
 
 
 
 
 
 
 
 
 
 
 
=> (x + 2sinx/2cosx/2)/(2cos^2x/2)dx => 0.5xsec^2x/2 dx + tanx/2 dx …..........................(1)

 
 
 
 
let tanx/2 = u
0.5sec^2x/2 dx = du
and x = vv
dx = dv
substittue in the eqn. (1)
and after integrating we get,
=> xtan(x/2) + c
 
Krish Gupta
askIITians Faculty 82 Points
3 years ago
 
∫(x+sinx)/(1+cosx)dx
 
 => write sinx and cosx in half angle formulaes:
 
 
 
 
 
 
 
 
 
 
 
=> (x + 2sinx/2cosx/2)/(2cos^2x/2)dx => 0.5xsec^2x/2 dx + tanx/2 dx …..........................(1)

 
 
 
 
let tanx/2 = u
0.5sec^2x/2 dx = du
and x = vv
dx = dv
substittue in the eqn. (1)
and after integrating we get,
=> xtan(x/2) + c∫(x+sinx)/(1+cosx)dx => write sinx and cosx in half angle formulaes: => (x + 2sinx/2cosx/2)/(2cos^2x/2)dx => 0.5xsec^2x/2 dx + tanx/2 dx …..........................(1) let tanx/2 = u 0.5sec^2x/2 dx = du and x = vv dx = dv substittue in the eqn. (1) and after integrating we get, => xtan(x/2) + c

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