Integral Of Te^t
How to find the integral of int(te^t, -e^(-2t), te^t(^2)) dt?
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nathanshields
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1. `int te^t dt`
Integrate by parts. u = t and dv = e^t. Then du = 1 and v = e^t
`=te^t-int e^t dt`
`=te^t-e^t+c`
`=e^t(t-1)+c`
2. `int -e^(-2t)dt`
You could use substitution, but I like to just think "what would the derivative of e^-2t be? -2e^-2t. So we have half of that:
`1/2 e^(-2t)+c`
3. `int te^(t^2) dt`
Think "what would the derivative of `e^(t^2)` be? `2te^(t^2)` . Again, we just have half of that in our integral, so answer is
`1/2e^(t^2)+c`
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