The conversation between human and AI assistant.
How can I solve: [math]\displaystyle\int \pi e^{2t}\cos\pi t+2e^{2t}\sin\pi t\;dt?[/math]
Can you help me solve this integral: [math]\displaystyle\int \pi e^{2t}\cos\pi t+2e^{2t}\sin\pi t\;dt?[/math]
Of course! First, we can use integration by parts to solve the integral. Let u be [math]\cos\pi t[/math] and dv be [math]\pi e^{2t}[/math] plus [math]2e^{2t}\sin\pi t[/math] dt.