Mathematics

# Evaluate:$\displaystyle \int \dfrac{dx}{(e^x + e ^{-x})}$

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

#### Realted Questions

Q1 Multiple Correct Medium
If $I=\sum _{ k=1 }^{ 98 }{ \displaystyle\int _{ k }^{ k+1 }{ \cfrac { k+1 }{ x(x+1) } } } dx$, then
• A. $I< \log _{ e }{ 99 }$
• B. $I< \cfrac{49}{50}$
• C. $I> \log _{ e }{ 99 }$
• D. $I> \cfrac{49}{50}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integral:
$\displaystyle\int^2_1\dfrac{dx}{x(1+log x)^2}$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following definite integral:
$\displaystyle \int _{-\pi /4}^{\pi /4} \dfrac {1}{1+\sin x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate: $\displaystyle \int_2^3 \cfrac{1}{x}dx.$

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.