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Question

If Im,n=10xm(logx)ndx, then Im,nit is equal to

A
nn+1Im,n1
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B
nm+1Im,n1
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C
1m+1Im,n1
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D
mn+1Im,n1
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Solution

The correct option is C 1m+1Im,n1
Im,n=10xm(logx)ndx
=[(logx)nxm+1m+1]1010n(logx)n11xxm+1(m+1)dx
=0n(m+1)10xm(logx)n1dx
=nm+1Im,n1

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