Indefinite integrals make no sense without specifying types. However, you may
take the definite integral.
(1) -> integrate(f,x=u..v)
a u 2 a v 4 a u 4 a v 2 a u 2
(%e ) (%e ) + (- (%e ) - 1)(%e ) + (%e )
(1) ------------------------------------------------------
a u 2 a v 2
8 a (%e ) (%e )
Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
(2) -> limit(%,a=0)
(11) 0
Type: Union(OrderedCompletion(Expression(Integer)),...)
(2) ->
Better would be anyway (use functions (==) instead of Expression (:=))
(5) -> h(a,x)== cosh(a * x) * sinh(a * x)
Type: Void
(6) -> integrate(h(a,x),x)
Compiling function h with type (Variable(a), Variable(x)) ->
Expression(Integer)
2 2
sinh(a x) + cosh(a x)
(6) -----------------------
4 a
Type: Union(Expression(Integer),...)
(7) -> integrate(h(0,x),x)
Compiling function h with type (NonNegativeInteger, Variable(x)) ->
Expression(Integer)
(7) 0
Type: Union(Expression(Integer),...)
You certainly know from calculus that
(9) -> integral(f,x)
x
++
(9) | cosh(%A a)sinh(%A a)d%A
++
Type: Expression(Integer)
is not necessarily continuous in "a" ;)
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