1. The problem is to solve the integral without using substitution. 2. The integral is not explicitly given, so let's assume a common integral that often requires substitution, for example, $$\int x e^{x^2} \, dx$$. 3. Normally, substitution $u = x^2$ is used, but since substitution is not allowed, we use integration by parts. 4. Recall the integration by parts formula: $$\int u \, dv = uv - \int v \, du$$. 5. Let $u = x$ and $dv = e^{x^2} dx$. However, $dv = e^{x^2} dx$ does not have an elementary antiderivative, so integration by parts is not straightforward here. 6. Without substitution or integration by parts, this integral cannot be expressed in elementary functions. 7. Therefore, the integral $$\int x e^{x^2} \, dx$$ without substitution is not solvable in elementary terms. 8. If you provide the exact integral, I can attempt to solve it without substitution if possible.