If ∫$$x2$$⋅e−$$2xdx=e$$−$$2xax2+bx+c+d$$, then

Correct option is 1a=1,b=1,c=12

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$If \int x^{2} \cdot e^{- 2 x} d x = e^{- 2 x} (a x^{2} + b x + c) + d, then$

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a=1,b=1,c=12

a=1,b=−1,c=−12

a=1,b=−1,c=12

None of these

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detailed solution

Correct option is A

∫x2⋅e−2xdx=e−2xax2+bx+c+d Differentiating both sides, we get x2⋅e−2x=e−2x(2ax+b)+ax2+bx+c−2e−2x=e−2x−2ax2+2(a−b)x+b−2c⇒ a=1,2(a−b)=0,b−2c=0⇒b=1,c=12

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If ∫x2⋅e−2xdx=e−2xax2+bx+c+d, then

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$If \int x^{2} \cdot e^{- 2 x} d x = e^{- 2 x} (a x^{2} + b x + c) + d, then$