How do you use integration by parts to find intxe^-x dx∫xe−xdx?

1 Answer
Gaurav
Jul 28, 2014

=-e^-x(1+x)+c=−e−x(1+x)+c, where c is a constant

Explanation

Using Integration by Parts,

int(I)(II)dx=(I)int(II)dx-int((I)'int(II)dx)dx

where (I) and (II) are functions of x, and (I) represents which will be differentiated and (II) will be integrated subsequently in the above formula

Similarly following for the problem,

=x*inte^-xdx-int((x)'inte^-xdx)dx

=x*e^-x/(-1)+inte^-xdx

=-x*e^-x+e^-x/(-1)+c, where c is a constant

=-x*e^-x-e^-x+c, where c is a constant

=-e^-x(1+x)+c, where c is a constant

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