##### solve that using this formula UV-VDU

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using integration by parts solve the integral -6xe^(-2)  solve that using this formula UV-VDU

Oct 27th, 2015

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Since 6 and e^(-2) are constants and x is only function in x, we actually do not need to use integration by parts.

Without using integration by parts:

$\\ \int -6xe^{-2}dx\\ \\ =-6e^{-2}\int xdx\\ \\ =-6e^{-2}\times\frac{x^2}{2}+c\\ \\ =-3e^{-2}x^{2}$

Using integration by parts: (u = x, v = 1)

$\\ \int -6xe^{-2}dx\\ \\ =-6e^{-2}\int x\cdot1dx\\ \\ =-6e^{-2}\bigg[x\int1dx-\int\bigg(\frac{d}{dx}(x)\cdot\int1dx\bigg)dx\bigg]\\\\ \\ \\ =-6e^{-2}\bigg[x\cdot x-\int\bigg(1\cdot x\bigg)dx\bigg]+c\\ \\ =-6e^{-2}\bigg[x^2-\int xdx\bigg]+c\\ \\ =-6e^{-2}\bigg[x^2-\frac{x^2}{2}\bigg]+c\\ \\ =-6e^{-2}\times\frac{x^2}{2}+c\\ \\ =-3e^{-2}x^{2}+c$

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Oct 27th, 2015

I forgot to add the constant of integration in the last step(Without using integration by parts). Please add that.

$=-3e^{-2}x^{2}+c$

Oct 27th, 2015

thank you for your reply, i was able to gifure most of it out on my own. for future reference if I use this service again cn we talk one on one live? or is it always I submit and then you reply

Oct 27th, 2015

Yes there is chat available which you can use to ask doubts. But for solving questions you would have to submit a question like this.

Oct 27th, 2015

Good night :)

Oct 27th, 2015

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