The correct option is A e^x[3x^2+x+1] +c ∫ e^x(3x^2+7x+2)dx 3∫ e^xx^2 dx+7 ∫ e^xx dx+2∫ e^xdx ∫ e^x x^2 dx=x^2e^x 2∫ xe^x dx+c ∫ xe^x= ...

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Integration by Parts

∫ ex3x2+7x+2d...

Question

$\int e^{x} (3 x^{2} + 7 x + 2) d x =$

e^{x} [3 x^{2} + x + 1] + c

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e^{x} [3 x^{2} + 7 x + 1] + c

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e^{x} [3 x^{2} - x - l] + c

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e^{x} [3 x^{2} + x] + c

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Solution

The correct option is A $e^{x} [3 x^{2} + x + 1] + c$
$\int e^{x} (3 x^{2} + 7 x + 2) d x$
$3 \int e^{x} x^{2} d x + 7 \int e^{x} x d x + 2 \int e^{x} d x$
$\int e^{x} x^{2} d x = x^{2} e^{x} - 2 \int x e^{x} d x + c$
$\int x e^{x} = x e^{x} - e^{x} + c$
$\int e^{x} = e^{x} + c$
$3 [x^{2} e^{x}] - 6 \int x e^{x} d x + 7 \int e^{x} - x d x + 2 e^{x}$
$3 x^{2} e^{x} + x e^{x} - e^{x} + e^{x} + 2 e^{x} + c$
$= e^{n} [3 x^{2} + x + 1] + c$
$\int e^{x} (3 x^{2} + 7 x + 2) d x = e^{x} [3 x^{2} + x + 1] + c$

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