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Question

Evaluate x4(5+4x)(x5+x+1)2dx

A
1x5+x+1+c
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B
x4+xx5+x+1+c
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C
5x4x5+x+1+c
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D
x5x5+x+1+c
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Solution

The correct option is D x5x5+x+1+c
I=x4(5+4x)(x5+x+1)2dxI=x4(5+4x)x10(1+x4+x5)2dxI=(5x4+4x5)x10(1+x4+x5)2dx
I=5x6+4x5(1+x4+x5)2dx
Put (1+x4+x5)=t(5x6+4x5)dx=dt

I=dtt2=1t+c
I=11+x4+x5+c

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