Mathematics

Solve $$\displaystyle\int\dfrac {(1+\log x)^{2}}{x}dx$$


SOLUTION
$$\displaystyle\int\dfrac {(1+\log x)^{2}}{x}dx$$
Put, $$1+\log x = t$$

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

Now, $$\displaystyle\int \dfrac{(1 + \log x)^2}{x} dx $$

$$= \int t^{2} dt $$

$$= \dfrac{t^{3}}{3} + c$$

$$= \dfrac{(1+\log x)^{3}}{3} + c$$
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 Subjective Medium
solve the following.
$$\int\limits_0^1 {\frac{{\log (1 + t)}}{{(1 + {t})^2}}} dt$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Hard
Value of $$\displaystyle \int_{-\pi /2}^{\pi /2}\cos ^{3}x \left ( 1+\sin x  \right )^{2}\: dx $$ is
  • A. $$4/5$$
  • B. $$6/5$$
  • C. $$2$$
  • D. $$8/5$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Write a value of 
$$\int { \log _{ e }{ x }  } dx\quad $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Hard
Evaluate: $$\displaystyle \int_{0}^{\pi}\frac{dx}{5+4\cos x}$$
  • A. $$\dfrac{\pi}{2}$$
  • B. $$\dfrac{\pi}{6}$$
  • C. $$-\pi$$
  • D. $$\dfrac{\pi}{3}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Single Correct Medium
If $$y = \frac{1}{x}$$, then value of $$\int \ ydx$$ is
  • A. $$log_{10}x+c$$
  • B. $$log_e \Big \lgroup \frac{1}{x} \Big \rgroup + c$$
  • C. $$log_{10} \Big \lgroup \frac{1}{x} \Big \rgroup + c$$
  • D. $$log_ex + c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer