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Question

xex(1+x)2dx is equal to

A
exx+1+C
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B
exx+1+C
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C
xexx+1+C
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D
xexx+1+C
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E
ex(x+1)2+C
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Solution

The correct option is E exx+1+C
Let I=xex(1+x)2dx

I=(x+11)ex(1+x)2dx

I=ex(1+x)dxex(1+x)2dx
Applying integration by parts in first integral, we get
I=ex(1+x)(1(1+x)2)exdxex(1+x)2dx+C

I=ex(1+x)+(1(1+x)2)exdxex(1+x)2dx+C
I=ex(1+x)+C

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