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integral of exp(-x/a)*sinh(sqrt(b*x)) from 0 to infinity vanished?

Hi there.

I've tried to calculate integral, 0exp(x/a)sinh(bx)dx,

a, b = var("a b")
Watt = exp(-x/a)*sinh(sqrt(b*x))
defInt = integrate(Watt,x,0,infinity)

For a>0 and b>0, the result seems to be πa3/2beab/42, and actually

defInt_a1_b1 = integrate(Watt(a=1,b=1),x,0,infinity)
defInt_a1_b1.full_simplify()

yields 12πe14.

But

defInt = integrate(Watt,x,0,infinity)
defInt

vanishes... 0

Where did I make mistakes?

Thanks in advance,

Kazuyoshi