Mathematics

# The value of $\int { \frac { dx }{ \left( { e }^{ x }+1 \right) \left( { 2e }^{ x }+3 \right) } }$ is equal to

$x+ In x+In\left( { e }^{ x }+1 \right) -\frac { 2 }{ 3 } In\left( { 2e }^{ x }+3 \right) +c$

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Single Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

#### Realted Questions

Q1 Subjective Medium
$\int { \dfrac { dx }{ { x }^{ { 1 }/{ 2 } }+{ x }^{ { 1 }/3 } } }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int \left\{\dfrac{(log x-1)}{1+(log x)^2}\right\}^2dx$ is equals to?
• A. $\dfrac{log x}{(log x)^2+1}+C$
• B. $\dfrac{x}{x^2+1}+C$
• C. $\dfrac{xe^x}{1+x^2}+C$
• D. $\dfrac{x}{(log x)^2+1}+C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate: $\displaystyle \int_{0}^{1} \cos$ $\left(2 \cot^{-1}\sqrt{\displaystyle \frac{1- {x}}{1+ {x}}}\right)dx$
• A. $\dfrac{1}{2}$
• B. $0$
• C. $1$
• D. $\dfrac{-1}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve:
$\int {\frac{{dx}}{{x + {x^{ - 3}}}}}$

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.