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Integration

Using Integration by parts

Intergrate this

(x*2 e*x dx)

Assuming that you mean x^2 and e^x

u = x²
dv/dx = e^x

INT(u.dv/dx) = uv - INT(v.du/dx)

du/dx = 2x
v = e^x

INT(x^2.e^x) = x^2.e^x - INT(2x.e^x) (i)

Now we must integrate 2x.e^x

u = 2x
dv/dx = e^x

INT(u.dv/dx) = uv - INT(v.du/dx)

du/dx = 2
v = e^x

INT(2x.e^x) = 2x.e^x - INT(2.e^x)

Now simply integrate 2e^x, which is e^(2x)

And thus INT(2x.e^x) = 2x.e^x - e^(2x) (ii)

Substituting (ii) into (i)

INT(x^2.e^x) = x^2.e^x - 2x.e^x - e^(2x)
INT(x^2.e^x) = e^x(x^2 - 2x - e^x)

There may be a constant of integration on the end as well ...

Reply 2

arktos

The_scholar

Using Integration by parts

Intergrate this

(x*2 e*x dx)

let u = x^2 du/dx = 2x

let dv/dx = e^x v = e^x

integral u.dv/dx = v.u. - integral (v . du/dx)

= e^x (x^2) - integral (2x. e^x)

let u = 2x du/dx = 2

let dv/dx = e^x v = e^x

=e^x (x^2) - [ (2xe^x - integral (2e^x)
=e^x(x^2) - 2x.e^x + 2e^x
=e^x (x^2 - 2x + 2) I think