EduFarming
Your list · 0हिं

Type at least two letters. Press Esc to close.

↑↓ navigate↵ openTAB cycle filter

Indefinite Integrals · Question 26 of 90

Question 26

MediumOriginal question

Evaluate ∫log⁡xx dx\int \frac{\log x}{x}\,dx.

Options for question 26

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Put t=log⁡xt = \log x, so dt=dxxdt = \frac{dx}{x}.

  2. ∫t dt=t22=(log⁡x)22+C\int t\,dt = \frac{t^{2}}{2} = \frac{(\log x)^{2}}{2} + C.

Worth noting

(log⁡x)2(\log x)^{2} forgets to divide by 2; its derivative is 2log⁡xx\frac{2\log x}{x}.

Concept
Substituting log x
Typical time
90 s
Your time
—
The rule this testsIntegration by substitution
Practise this chapter →

Ten questions from Indefinite Integrals, at your own pace.

Practise this chapter →

Ten questions from Indefinite Integrals, at your own pace.