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]
I see, then what do we do next?
Let's start with [math]u=\cos\pi t[/math], and find [math]du[/math]. Differentiating [math]\cos\pi t[/math] gives us [math]\frac{d}{dt}\cos\pi t = -\pi \sin\pi t[/math], so [math]du=-\pi\sin\pi t\, dt[/math].