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Question

If 1/21/8[ln[1x]]dx is equal to ab, where a and b are coprime, then the value of b4a is
([.] denotes the greatest integer function)

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Solution

I=1/21/8[ln[1x]]dx=1/71/8[ln7]dx+1/61/7[ln6]dx+1/51/6[ln5]dx+1/41/5[ln4]dx+1/31/4[ln3]dx+1/21/3[ln2]dx

Since [ln2]=0 and [ln3]=[ln4]=[ln5]=[ln6]=[ln7]=1
I=1/31/81 dx=524
a=5,b=24b4a=4

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