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## Integrals from ?inttrans[fourier]

Answering to Definite Integral post, I tried to do the first example in ` ?inttrans[fourier]`,
```assume(a>0):
inttrans[fourier](3/(a^2 + t^2),t,w);

Pi (exp(a~ w) Heaviside(-w) + exp(-a~ w) Heaviside(w))
3 ------------------------------------------------------
a~```
using int,
```int(3/(a^2+t^2)*exp(-I*w*t),t=-infinity..infinity);

0```
No comment. Well, I tried another example from the same help page,
```inttrans[fourier](1/(4 - I*t)^(1/3),t,2+w);

1/2
3    GAMMA(2/3) exp(-8 - 4 w) Heaviside(2 + w)
----------------------------------------------
2/3
(2 + w)

int(1/(4 - I*t)^(1/3)*exp(-I*t*w),t=-infinity..infinity);

/
1/3  1/2            |         1/2              1/3
- 1/4 I 2    3    GAMMA(2/3) |1/10 Pi 3    (-1 + 12 w) 2
|
\

/              1/3
exp(-2 w) WhittakerM(2/3, 5/6, 4 w)  /  (GAMMA(2/3) w   )
/

1/2  1/3
Pi 3    2    exp(-2 w) WhittakerM(5/3, 5/6, 4 w)
+ 3/5 ------------------------------------------------
1/3
GAMMA(2/3) w

\
1/2      (1/3)  (2/3)     (1/6)          |
+ 2/3 Pi 3    (w I)      2      (-1)      exp(-4 w)|/(Pi w)
|
/

/
1/3  1/2            |         1/2              1/3
+ 1/4 I 2    3    GAMMA(2/3) |1/10 Pi 3    (-1 + 12 w) 2
|
\

/              1/3
exp(-2 w) WhittakerM(2/3, 5/6, 4 w)  /  (GAMMA(2/3) w   )
/

1/2  1/3
Pi 3    2    exp(-2 w) WhittakerM(5/3, 5/6, 4 w)
+ 3/5 ------------------------------------------------
1/3
GAMMA(2/3) w

\
1/2       (1/3)  (2/3)     (5/6)          |
- 2/3 Pi 3    (-I w)      2      (-1)      exp(-4 w)|/(Pi w)
|
/

evalf(eval(%,w=1))=evalf(eval(%%,w=1));

-5
0.04295751906 + 0. I = 0.6927914186 10```
Again I'm silent. OK, another integral from the same page,
```inttrans[fourier](BesselJ(0,4*(t^2 + 1)^(1/2)), t, s);
2                                          /
8 exp(s I) cos(-16 + s ) (Heaviside(s + 4) - Heaviside(s - 4))  /
/

2 1/2
(16 - s )

int(BesselJ(0,4*(t^2 + 1)^(1/2))*exp(-I*t*w),t=-infinity..infinity);

infinity
/
|                         2     1/2
|          BesselJ(0, 4 (t  + 1)   ) exp(-I w t) dt
|
/
-infinity```
That's better - the integral is unevaluated, but at least the answer is not wrong.

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