Mathematics

$$\displaystyle\int \dfrac{\log x}{x} dx$$ is equal to


SOLUTION
$$I=\displaystyle\int \dfrac{\log x}{x} dx$$

Let $$\log x =t$$

$$\dfrac{1}{x}dx=dt$$

Therefore,
$$I=\int t \ dt$$

$$I=\dfrac{t^2}{2}+C$$

$$I=\dfrac{(\log x)^2}{2}+C$$
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
$$\displaystyle \int \frac {dx}{x\sqrt{x^6-1}} =$$
  • A. $$\frac {1}{3}cosec ^{-1}(x^3) +C$$
  • B. $$\frac {1}{3}cot^{-1}(x^3)+C$$
  • C. none of these
  • D. $$\frac {1}{3} sec^{-1}(x^3) +C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
Evaluate the integral
$$\displaystyle \int_{0}^{\pi_/{2}}\frac{secx}{secx+co\sec x}dx $$
  • A. $$\pi/3$$
  • B. $$\pi/2$$
  • C. $$\pi/8$$
  • D. $$\pi/4$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
The value of $$\displaystyle \int_{-2}^{2}(ax^{3}+bx+c)\ dx$$ depends on:
  • A. The value of $$b$$
  • B. The value of $$a$$
  • C. The value of $$a$$ and $$b$$
  • D. The value of $$c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Evaluate $$\int {\frac{{dx}}{{x\left( {{x^5} + 1} \right)}}} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
$$\int \frac{2x^{2}}{3x^{4}2x} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer