Mathematics

# The value of $\int_{0}^{1}\dfrac{dx}{e^{x}+e^{-x}}$ is

$\tan^{-1}\left(\dfrac{1-e}{1+e}\right)$

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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: $\displaystyle \overset{\frac{\pi}{2}}{\underset{0}{\int}} \sqrt{\cos \theta}\cdot \sin^3 \theta d\theta$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Find the general solution of $\frac{{dy}}{{dx}} = \frac{{2y}}{x}$
• A. $y=e^{5\log x +c}$
• B. $y=e^{3\log x +c}$
• C. None of these
• D. $y=e^{2\log x +c}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Evaluate $\displaystyle\int\displaystyle\dfrac{1}{e^x-1}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
If $\displaystyle \int\frac{2Cosx-3Sinx}{3Sinx+2Cosx}dx= A \log|3sinx+$$2cosx|+ BX+C$, then $A=\ldots\ldots\ldots.,B=\ldots\ldots\ldots\ldots$,
• A. $\displaystyle \frac{1}{13}, -\displaystyle \frac{5}{13}$
• B. $\displaystyle 12, -\displaystyle \frac{5}{13}$
• C. $\displaystyle \frac{12}{13},\frac{5}{13}$
• D. $\displaystyle \frac{12}{13},-\frac{5}{13}$

$\displaystyle \int \dfrac {1}{(x + 3)\sqrt {x + 2}}dx$, on $x\, \in I \subset (-2, \infty)$