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How can I solve: [math]\displaystyle\int \pi e^{2t}\cos\pi t+2e^{2t}\sin\pi t\;dt?[/math]
Alright, then what's next?
Next, we will integrate the remaining integral, which is [math]\int\left(\frac{1}{2}e^{2t}-\frac{1}{\pi}\cos\pi t\right)(-\pi\sin\pi t)\, dt[/math]. To do that, first let's simplify the expression to get: [math]-\frac{\pi}{2}e^{2t}\sin\pi t + \frac{1}{\pi}\cos^2\pi t[/math].