# How to find integrals including certain expression

how do I find some terms in an integral containing some expression, e.g. in

$$\int \int \int \beta\phi(x,y,z) + \gamma\omega(x,y,z)\,\textrm{d}x\textrm{d}y \textrm{d}z +\int \int \alpha\phi(x,y,z) + \gamma\theta(x,y,z)\,\textrm{d}x\textrm{d}y$$

only the term including $$\phi(x,y,z)$$ (incl. integrals), meaning:

$$\int \int \int \beta\phi(x,y,z) \textrm{d}x \textrm{d}y \textrm{d}z +\int \int \alpha\phi(x,y,z) \textrm{d}x\textrm{d}y\quad?$$

The approaches I found online so far don't work, help would be greatly appreciated.

• What approaches have you tried? What is the problem with the code you’re using? Is this a question about the software Mathematica? You can get help with a mathematics problem at math.stackexchange.com. – creidhne Dec 20 '20 at 15:20
• I meant how do I achieve this with Mathematica? I've tried different approaches with Select, MemberQ, Coefficient, etc. – MathsNoob69 Dec 20 '20 at 15:25

(int1 = Integrate[β ϕ[x, y, z] + γ ω[x, y, z], z, y, x] +
Integrate[α ϕ[x, y, z] + γ θ[x, y, z], y, x]) //


(int2 = int1 /. {_ω :> 0, _θ :> 0}) // TraditionalForm


Or

(int3 = int1 /.
Integrate[a_*phi_ϕ + b___, var__] :>

int2 === int3

• This unfortunately is not what I meant, as I don't actually know what the other terms look like - $\omega$ and $\Theta$ were just placeholders. – MathsNoob69 Jan 2 at 18:22