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 is [math]uv[/math]?
We can now plug in [math]u[/math] and [math]v[/math] into the equation [math]uv - \int v\, du[/math], which gives us: [math]\cos\pi t\left(\frac{1}{2}e^{2t}-\frac{1}{\pi}\cos\pi t\right)-\int\left(\frac{1}{2}e^{2t}-\frac{1}{\pi}\cos\pi t\right)(-\pi\sin\pi t)\, dt[/math].