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Question

Evaluate (lnx)x(ln(lnx)+1lnx)dx
(where C is constant of integration)

A
(lnx)x+C
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B
(lnx)x+C
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C
(lnx)x+C
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D
(lnx)x+C
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Solution

The correct option is A (lnx)x+C
Let I=(lnx)x(ln(lnx)+1lnx)dx
Put (lnx)x=t
(lnx)x(ddx(xln(lnx)))dx=dt
(lnx)x(ln(lnx)+xlnx1x)dx=dt
(lnx)x(ln(lnx)+1lnx)dx=dt
I=dt=t+C=(lnx)x+C

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