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I have to evaluate $\frac{1}{\tau} \int\limits_0^\tau{{(e^{\alpha t}-1)e^{-\beta t}}}dt$ , where ατ=1.

I did he following:

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But they have the following answer:

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Have I forgotten something? I did it multiple times. Can't get nearer to their result.

I apologize for not posting everything at once.

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