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Question

The derivative of x4+x5 is (4x5+5x6). So, 5x4+4x5(x5+x+1)2dx is equal to

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

The correct option is D x5x5+x+1+c
5x4+4x5(x5+x+1)2dx
=5x4+4x5x10(1+x4+x5)2dx
=(5x6+4x5)(1+x4+x5)2dx
=d(x5+x4+1)(1+x4+x5)2dx
=1(1+x4+x5)+c [ Where c being integrating constant]
=x5(1+x+x5)+c

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