Integration of (v/(root of 1+v^2/c^2) dv
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I = v.dv/√(1 + v²/c²)
Let v = ctanx
differentiate with respect to x
dv = c.sec²x.dx
I = c.tanx.c.sec²x.dx/√(1 + tan²x)
= c².tanx.sec²x.dx/secx
= c².tanx.secx.dx
= c².secx + Q
where Q is constant .
v = c.tanx
secx = √(1 + tan²x)
= √(1 + v²/c²)
so, I = c².√(1 + v²/c²) + Q
Let v = ctanx
differentiate with respect to x
dv = c.sec²x.dx
I = c.tanx.c.sec²x.dx/√(1 + tan²x)
= c².tanx.sec²x.dx/secx
= c².tanx.secx.dx
= c².secx + Q
where Q is constant .
v = c.tanx
secx = √(1 + tan²x)
= √(1 + v²/c²)
so, I = c².√(1 + v²/c²) + Q
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