allery$\int \log x\,dx$ equals
A$x\log x+x+C$
B$\dfrac{1}{x}+C$
C$x\log x-x+C$
D$\log x-x+C$
Answer & Solution
Correct answer: C. $x\log x-x+C$
1. Take $u=\log x$ (first), $dv=1\,dx$, so $v=x$.
2. By parts: $x\log x-\int x\cdot\dfrac{1}{x}\,dx$.
3. $=x\log x-\int 1\,dx=x\log x-x+C$.
4. Differentiating: $\log x+1-1=\log x$, confirming C.
_Source: syllabus Mathematics Ch 7 "Integrals", p.325_
Keep practising Probability & Statistics
Browse all Probability & Statistics questions for GMAT, or explore more Mathematics topics.
Related questions
True or false: reading the identitiesRadians and degreesOn a given day the chance of rain is 0.4. When it rains, the chance a match is called off Two ordinary six-sided dice are rolled. What is the probability that the two numbers add uTwo events are independent. What does knowing that one of them happened tell you about theA bag holds 3 red balls, 5 blue balls and 2 yellow balls. What is the chance of drawing a Mutually exclusive events can never do what?What is the set of all possible outcomes of an experiment called?