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Mathematics
Makena Hood
14 October, 13:18
Evaluate the integral: integral of t sinh mt dt
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Hugo West
14 October, 13:55
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Integrate by parts
f = t, df = dt,
dg = sinh (mt) dt
g = cosh (mt) / m
put them together
tcosh (mt) / m - / m * ∫cosh (mt) dt
u = mt, du = mdt
tcosh (mt) / m - / m^2 * ∫cosh (u) dt
integral of cosh (u) = sinh (u)
tcosh (mt) / m - sinh (u) / m^2 + c1
substitute back in the u (mt)
tcosh (mt) / m - sinh (mt) / m^2 + c1
You can simplify this
((mt*cosh (mt) - sinh (mt))) / m^2
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