How do you find the antiderivative of $((2x)e^(3x))$ ?

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Answer 1 · 2016-08-03T13:18:44

$1/9*(3x-1)*e^(3x)+C$ .

Let, $I=int2xe^(3x)dx rArr I=2intxe^(3x)dx$ .

To find $I$ , we will use the following Rule of Integration by Parts :

$intuvdx=uintvdx-int{(du)/dxintvdx}dx$ .

We take, $u=x, so, (du)/dx=1, &, v=e^(3x), so, intvdx=1/3e^(3x)$ . So,

$I=x*1/3e^(3x)-int{1*1/3e^(3x)}dx$

$=x/3e^(3x)-1/3inte^(3x)dx$

$=x/3e^(3x)-1/3*1/3e^(3x)$

$:. I = 1/9*(3x-1)*e^(3x)+C$ .

How do you find the antiderivative of ((2x)e^(3x))((2x)e^(3x))?