Q. $\int e^{x} \cdot x^{5} d x$ is

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A

$e^{x}\left[x^{5}+5 x^{4}+20 x^{3}+60 x^{2}+120 x+120\right]+c$

B

$e^{x}\left[x^{5}-5 x^{4}-20 x^{3}-60 x^{2}-120 x-120\right]+c$

C

$e^{x}\left[x^{5}-5 x^{4}+20 x^{3}-60 x^{2}+120 x-120\right]+c$

D

$e^{x}\left[x^{5}+5 x^{4}+20 x^{3}-60 x^{2}-120 x+120\right]+c$

Solution:

$\int e^{x} x^{5} d x=x^{5} e^{x}-e^{x} \cdot 5 x^{4}+e^{x} \cdot 20 x^{3}-e^{x}, 60 x^{2}+e^{x} \cdot 120 x-e^{x} \cdot 120+c$.(by Bernoullis rule) $= e ^{x}\left[ x ^{5}-5 x ^{4}+20 x ^{3}-60 x ^{2}+120 x -120\right]+ c$

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