Julia - Compute exact integral depending on constants

Question

With MTH229 you can compute integrals with different possibilities. However, what if I want to compute one depending on a constant?

For instance:

integrate(x->x^3, 0, 1) 

works perfectly. As well as:

integrate(x->x^3)

But what if I want to compute the exact value depending of C which is a real constant of this following:

integrate(x->C*x^3) # Obviously doesn't work as C isn't defined.

Note 1: I here use a much simplified function to integrate, the one I need is a polynomial with other degrees and more complicated coefficients.

Note 2: Thus I only use one constant C , but actually, I have several, C1, C2, C3 etc.

Note 3: I am not closed to MTH229 package. Any Julia package working will be fine :)

EDIT: Actually, what I'm looking is to compute an integral with additional parameters as possible in Python-Scipy but with exact expression (and not evaluated within 0 and 1 like the following picture):

Answer 1

That integrate is no more than a wrapper around SymPy's integrate for Function objects. To do what you want you need to uses SymPy 's syntax:

using SymPy # this happens behind the scenes when you load MTH229
@vars x a b # defined some variables
integrate(a*x^2 + b, x)  # indefinite integral needs variable to integrate in specified
integrate(a*x^2 + b, (x, 0, 1)) # definite integral example