∫ lnxdx = - - - - - -?
- xlnx – x + c
- xlnx + x + c
- 1/x
- None of these
Explanation
To find ∫ln(x)dx, we use integration by parts:
Let u = ln(x) and dv = dx
Then du = 1/x dx and v = x
∫ln(x)dx = uv - ∫v du
= x_ln(x) - ∫x * 1/x dx
= x_ln(x) - ∫1 dx
= x*ln(x) - x + C
The answer is xlnx – x + c.
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