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

Hi there.

I've tried to calculate integral, $$\int_{0}^{\infty} \exp{(-x/a)}\:\sinh{(\sqrt{bx})}\:dx,$$

```
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 $$\frac{\sqrt{\pi}\:a^{3/2}\:\sqrt{b}\:e^{ab/4}}{2},$$ and actually

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

yields $$\frac{1}{2}\sqrt{\pi}\:e^{\frac{1}{4}}.$$

But

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

vanishes... $$0$$

Where did I make mistakes?

Thanks in advance,

Kazuyoshi

some issue in maxima. you can try other engines:

FWIW :

@FrédéricC :

I took the liberty of refoprmatting your comment, which you had formatted in markdown ;-)...

You should make an answer of your comment, for the benefiot of future (per-)users...

HTH,

Thanks @FrédéricC for your comment. Indeed,

yields 0.

But it seems to me that this is

notdue to Maxima itself because direct run of Maxima from console (and via Jupyterlab Desktop) yields the expected result, $\frac{\sqrt{\pi}a^{3/2}\sqrt{b}e^{ab/4}}{2}$.I'll try other engines...

@Emmanuel Charpentier, thanks for your comment. Do I need to install extra/optional packages to do the following?:

When I did that I got (in short):

By the way I use SageMath 10.1 (from console as well as Jupyterlab Desktop) built from source, on Fedora linux 38 (x86_64).