Mathematics

# solve $\int \frac{1}{1+e^{-1}}\;dx$

##### SOLUTION
$\displaystyle\int \dfrac{1}{1+e^{-1}}d{x}=\dfrac{x}{1+e^{-1}}+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Subjective Medium
Find the integrals of the functions.
i) $sin^2 (2x + 5)$
ii) $sin \, 3x \, cos \, 4x$
iii) $cos \, 2x \, cos \, 4x \, cos \, 6x$
iv) $sin^3 (2x + 1)$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Simplify: $\int {\dfrac{{{e^x}\left( {x - 1} \right)}}{{{{\left( {x + 1} \right)}^3}}}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\tan^{-1}\left(\displaystyle \frac{3x-x^{3}}{1-3x^{2}}\right)$ can be integrated by substituting
• A. $x=\cos\theta$
• B. $x=\sin\theta$
• C. $x=\sec\theta$
• D. $x=\tan\theta$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int \frac{a}{b+ce^{x}}dx.$
• A. $\displaystyle \frac{a}{b}\left [ x+\log \left ( b+ce^{x} \right ) \right ].$
• B. $\displaystyle \frac{a}{b}\left [ x-\log \left ( ce^{x} \right ) \right ].$
• C. $\displaystyle \frac{a}{c}\left [ x+\log \left ( b+ce^{x} \right ) \right ].$
• D. $\displaystyle \frac{a}{b}\left [ x-\log \left ( b+ce^{x} \right ) \right ].$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
For the next two (02) items that follow :
Consider the integrals $I_1=\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{dx}{1+\sqrt{tan x}}$ and $I_2=\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\sqrt{sin x}dx}{\sqrt{sin }x+\sqrt{cos}x}$