Mathematics

# $\displaystyle \int \dfrac{e^{-x}}{1+ e^{-x}}dx$ $=$  $-p \log (1+e^{-x})+C$ then p =

1

##### SOLUTION

$Let\>1+e^{-x}=t\\\therefore\>-e^{-x}dx=dt\\\therefore\>\int\>(\frac{1}{t})dt\\=-logt+C\\=-log(1+e^{-x})+C$

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

#### Realted Questions

Q1 Single Correct Medium
Evaluate : $\displaystyle\int \frac{\cos \sqrt{x}}{\sqrt{x}}dx.$
• A. $\displaystyle \sin \sqrt{x}.$
• B. $\displaystyle 2\sin x.$
• C. $\displaystyle 2\sin \sqrt{x}/3.$
• D. $\displaystyle 2\sin \sqrt{x}.$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\displaystyle \int sin^{-1}\sqrt{\frac{x}{a+x}}dx=\ldots\ldots$
• A. $(a+x)tan^{-1} \sqrt{x/a}+\sqrt{ax}+c$
• B. $(a+x)cot^{-1} \sqrt{x/a}+\sqrt{ax}+c$
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1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integrals:$\displaystyle \int {\dfrac{3}{\sqrt{7x-2}-\sqrt{7x-5}}.dx}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
Evaluate : $\displaystyle \underset{0}{\overset{\infty}{\int}} \dfrac{dx}{(1 + x^2)^4}$
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