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# ∫(x+sinx)/(1+cosx)dx

Vikas TU
14149 Points
5 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
one year 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$%u222B(x+sinx)/(1+cosx)dx => write sinx and cosx in half angle formulaes: => (x + 2sinx/2cosx/2)/(2cos^2x/2)dx => 0.5xsec^2x/2 dx + tanx/2 dx %u2026..........................(1) let tanx/2 = u 0.5sec^2x/2 dx = du and x = vv dx = dv substittue in the eqn. (1) and after integrating we get, => xtan(x/2) + c$