Mathematics

# Evaluate the following integral:$\int { \log _{ x }{ x } } dx$

##### SOLUTION
Given $\displaystyle\int{\log_{x}{x}dx}$

$=\displaystyle\int{dx}$ since $\log_{x}{x}=1$

$=x+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Hard
$\displaystyle \int \frac{x^3dx}{\sqrt{1\, +\, x^2}}$ is equal to
• A. $\displaystyle \frac{1}{3}\, \sqrt{1\, +\, x^2}\, (2\, +\, x^2)\, +\, c$
• B. $\displaystyle \frac{1}{3}\, \sqrt{1\, +\, x^2}\, (x^2\, -\, 1)\, +\, c$
• C. $\displaystyle \frac{1}{3}\, (1\, +\, x^2)^{3/2}\, +\, c$
• D. $\displaystyle \frac{1}{3}\, \sqrt{1\, +\, x^2}\, (x^2\, -\, 2)\, +\, c$

1 Verified Answer | Published on 17th 09, 2020

Q2 One Word Medium
Evaluate:$\displaystyle \int \frac{dx}{\sqrt{8-4x-2x^{2}}}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate :
$\displaystyle\int{\dfrac { \left( logx \right) ^{ 2 } }{ x }dx}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle \int \frac{e^{x}(x+1)}{cos^{2}(xe^{x})}dx=$

• A. $sec (xe^x) tan (xe^x) + C$
• B. $-tan (xe^x) + C$
• C. None of these
• D. $tan (xe^x) + C$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$