Mathematics

# $\displaystyle\int \dfrac{1}{1+e^x}dx$ is equal to?

$log_e\left(\dfrac{e^x}{e^x+1}\right)+c$

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

$=-ln|1+e^{-x}|+c$

$=-ln\left|\dfrac{e^x+1}{e^x}\right|+c$

$=ln\left|\dfrac{e^x}{e^x+1}\right|+c$.

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Hard
Evaluate the following integrals:
$\displaystyle \int { \cfrac { \cos { x } }{ \sqrt { 4+\sin ^{ 2 }{ x } } } } dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\displaystyle \int_{-\pi}^{\pi}\frac{\cos^{2}x}{1+a^{\mathrm{x}}}dx,\ a>0$, is?
• A. $2\pi$
• B. $\displaystyle \frac{\pi}{a}$
• C. $a\pi$
• D. $\displaystyle \frac{\pi}{2}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\int_{0}^{f(x)} t^{2} d t=x \cos \pi x,$ then $f^{\prime}({9})$ is
• A. $-\dfrac{1}{3}$
• B. $\dfrac{1}{3}$
• C. non-existent
• D. $-\dfrac{1}{9}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 One Word Medium
If $\int \dfrac{1}{1+ \sin x} dx=\tan x-m\sec x$.Find $m$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Hard
Let $\displaystyle 2I_{1}+I_{2}=\int \frac {e^{x}}{e^{2x}+e^{-2x}}dx$  and  $\displaystyle I_{1}+2I_{2}=\int \frac {e^{-x}}{e^{2x}+e^{-2x}}dx$
On the basis of above information, answer the following questions :

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020