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Integration of exponential :( (2 Viewers)
- Thread starter enigma_1
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obliviousninja
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Isnt this by parts?
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Hint: consider the derivative of xex
seanieg89
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Yeah trebla's thing is part a. But i dunno what to do afterwards
enigma_1
~~~~ Miss Cricket ~~~~
fuarkkk legend. I suck at this manipulation stuff.=xe^x+e^x \\ \\ \Rightarrow \int xe^x\, dx = \int \frac{d}{dx}(xe^x) \, dx - \int e^x \, dx = (x-1)e^x + C.)
seanieg89
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In future, remember that most of the questions of this form (where they first get you to differentiate something, and then ask you to integrate something similar) follow a predictable pattern:
You want to write the function you are trying to integrate as the derivative of something (which will be closely related to your answer to the first part) + stuff. Where "stuff" is straightforward to integrate, and is even just 0 sometimes.
To practice this motif, differentiate x*log(x) and hence integrate log(x). (Where log is the natural logarithm.)
If you want still more practice, differentiate x*sin(x) and hence integrate x*cos(x).
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