- #1
lightarrow
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Homework Statement
L{sin(ωt)/[1+cos^2(ωt)]} =
Homework Equations
d {arctan[cos(ωt)]} /dt =
- ω•sin(ωt)/[1+cos^2(ωt)]
The Attempt at a Solution
∫e^(-st)•[sin(ωt)/(1+cos²(ωt)] dt =
-(1/ω)•∫e^(-st)•{arctan[cos(ωt)]}' dt =
= (integrating by parts and taking Re(s) > 0) =
= π/(4ω) -(s/ω)•∫ e^(-st)•arctan[cos(ωt)]
= π/(4ω) -(s/ω)•L{arctan[cos( ωt)]}.
But at this point I don't know how to compute the last laplace transform.
So I don't know if this is the best way or even if my question has a (simple) solution at all.
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lightarrow
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