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# sympy.integrals.meijerint.meijerint_definite

All Samples(36)  |  Call(32)  |  Derive(0)  |  Import(4)

```from sympy.integrals.rationaltools import ratint
from sympy.integrals.heurisch import heurisch, heurisch_wrapper
from sympy.integrals.meijerint import meijerint_definite, meijerint_indefinite
from sympy.utilities.misc import filldedent
```
```                    x, a, b = xab
try:
res = meijerint_definite(function, x, a, b)
except NotImplementedError:
from sympy.integrals.meijerint import _debug
```

```from sympy.integrals.rationaltools import ratint
from sympy.integrals.heurisch import heurisch, heurisch_wrapper
from sympy.integrals.meijerint import meijerint_definite, meijerint_indefinite
from sympy.utilities.misc import filldedent
```
```                    x, a, b = xab
try:
res = meijerint_definite(function, x, a, b)
except NotImplementedError:
from sympy.integrals.meijerint import _debug
```

```from sympy import (meijerg, I, S, integrate, Integral, oo, gamma,
hyperexpand, exp, simplify, sqrt, pi, erf, sin, cos,
exp_polar, polar_lift, polygamma, hyper, log, expand_func)
from sympy.integrals.meijerint import (_rewrite_single, _rewrite1,
meijerint_indefinite, _inflate_g, _create_lookup_table,
```
```    # This tests "extra case" for antecedents_1.
a, b = symbols('a b', positive=True)
assert simplify(meijerint_definite(x**a, x, 0, b)[0]) == \
b**(a + 1)/(a + 1)

# This tests various conditions and expansions:
meijerint_definite((x + 1)**3*exp(-x), x, 0, oo) == (16, True)
```
```    # Again, how about simplifications?
sigma, mu = symbols('sigma mu', positive=True)
i, c = meijerint_definite(exp(-((x - mu)/(2*sigma))**2), x, 0, oo)
assert simplify(i) == sqrt(pi)*sigma*(erf(mu/(2*sigma)) + 1)
assert c == True

i, _ = meijerint_definite(exp(-mu*x)*exp(sigma*x), x, 0, oo)
```

```from sympy import (meijerg, I, S, integrate, Integral, oo, gamma,
hyperexpand, exp, simplify, sqrt, pi, erf, sin, cos,
exp_polar, polar_lift, polygamma, hyper, log, expand_func)
from sympy.integrals.meijerint import (_rewrite_single, _rewrite1,
meijerint_indefinite, _inflate_g, _create_lookup_table,
```
```    # This tests "extra case" for antecedents_1.
a, b = symbols('a b', positive=True)
assert simplify(meijerint_definite(x**a, x, 0, b)[0]) == \
b**(a + 1)/(a + 1)

# This tests various conditions and expansions:
meijerint_definite((x + 1)**3*exp(-x), x, 0, oo) == (16, True)
```
```    # Again, how about simplifications?
sigma, mu = symbols('sigma mu', positive=True)
i, c = meijerint_definite(exp(-((x - mu)/(2*sigma))**2), x, 0, oo)
assert simplify(i) == sqrt(pi)*sigma*(erf(mu/(2*sigma)) + 1)
assert c is True

i, _ = meijerint_definite(exp(-mu*x)*exp(sigma*x), x, 0, oo)
```