Question

Integration of e^x(x²+2x)

Answer 1

Answer :

Now, ∫ eˣ (x² + 2x) dx

= (x² + 2x) ∫ eˣ dx - ∫ [$\frac{d}{dx}$ (x² + 2x) × ∫ eˣ dx ] dx

= (x² + 2x) eˣ - 2 ∫ (x + 1) eˣ dx

= (x² + 2x) eˣ - 2 (x + 1) ∫ eˣ dx

+ 2 ∫ [$\frac{d}{dx}$(x + 1) × ∫ eˣ dx ] dx

= (x² + 2x) eˣ - 2 (x + 1) eˣ + 2 ∫ eˣ dx + c,

where c is integral constant

= (x² + 2x - 2x - 2 +2 ) eˣ + c

= x² eˣ + c

#MarkAsBrainliest

Answer 2

HELLO FRIEND HERE IS YOUR ANSWER,,,,,,

To find the integration of,,

$\int{e}^{x} ( {x}^{2} + 2x) dx$
Using the formula,,,,

$\int{uv}^{1} = uv - {u}^{1} v$

Therefore,,,

$u = ( {x}^{2} + 2x) \\ \\ {v}^{1} = {e}^{x}$

$( {x}^{2} + 2x) {e}^{x} - \int(( {x}^{2} + 2x)) {e}^{x} \\ \\ \\ ( {x}^{2} + 2x) {e}^{x} - \frac{d}{dx} ( {x}^{2} ) + 2 \frac{d}{dx} (x) \int{e}^{x} dx$

Check the attachment for further steps.

Note: Ignore my handwriting it's even worse than a sloth.

HOPE IT HELPS YOU AND CLEARS YOUR DOUBTS REGARDING INTEGRATIONS!!!