Mathematics

# The integral $\int_{2}^{4}{\frac {log x^{2}}{log x^{2} +log (36-12x+x^{2})}} dx$ is equal to :

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

#### Realted Questions

Q1 Subjective Hard
Solve $\displaystyle\int{\dfrac{6{u}^{3}du}{1+u}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve: $\displaystyle \int \dfrac{x^3}{x - 2}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\int\frac{dx}{x(x^n+1)}$
• A. ${n}$ $(log{x^n}$-$log(x^n +1))+C$
• B. $\frac{1}{n}$ $(log{x^n}$+$log(x^n +1))+C$
• C. ${n}$ $(log{x^n}$+$log(x^n +1))+C$
• D. $\frac{1}{n}$ $(log{x^n}$-$log(x^n +1))+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle\int{\frac{x^2(1-\ln{x})}{\ln^4{x}-x^4}dx}$ is equal to
• A. $\displaystyle\frac{1}{2}\ln{\left(\frac{x}{\ln{x}}\right)}-\frac{1}{4}\ln{(\ln^2{x}-x^2)}+C$
• B. $\displaystyle\frac{1}{4}\ln{\left(\frac{\ln(x)+x}{\ln{x}-x}\right)}-\frac{1}{2}\tan^{-1}{\left(\frac{\ln{x}}{x}\right)}+C$
• C. $\displaystyle\frac{1}{4}\left(\ln{\left(\frac{\ln(x)-x}{\ln{x}+x}\right)}+\tan^{-1}{\left(\frac{\ln{x}}{x}\right)}\right)+C$
• D. $\displaystyle\frac{1}{4}\ln{\left(\frac{\ln(x)-x}{\ln{x}+x}\right)}-\frac{1}{2}\tan^{-1}{\left(\frac{\ln{x}}{x}\right)}+C$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Let $n \space\epsilon \space N$ & the A.M., G.M., H.M. & the root mean square of $n$ numbers $2n+1, 2n+2, ...,$ up to $n^{th}$ number are $A_{n}$, $G_{n}$, $H_{n}$ and $R_{n}$ respectively.
On the basis of above information answer the following questions