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Question

10ln(1+x)1+x2dx=

A
π4ln2
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B
π2ln2
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C
π8ln2
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D
π ln2
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Solution

The correct option is A π4ln2
i(ln(1i))ln(1x+il)+ln(i+1)ln(1xil)+li2(x+ix1)li2(x+i1+i))+c2
arctan(x)ln(x+1)arctan|(x)ln(x2+2x+12)tan2(x+12,x+12)
ln(x2+1)ili2(ll(i+1)xi+12)+ili2(i(i+1)xi12)+c2

ili2(i+12)ili2(i12)+ili2(1)2i(li21)2+πln(2)42
=πln(2)4

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