Mathematics

# $\int {\frac{e^xdx}{e^x+1}}$

##### SOLUTION
$\int \cfrac{e^x}{e^x+1}dx$
Let  $e^x+1=z\implies e^x dx=dz$
$\int\cfrac{1}{z}dz$
$=\ln|z|+c$
$=\ln|e^x+1|+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

#### Realted Questions

Q1 Passage Medium
Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives

1 Verified Answer | Published on 17th 08, 2020

Q2 Single Correct Hard
Evaluate: $\displaystyle \int \dfrac{(x-1)e^x}{(x+1)^3}dx=$
• A. $\dfrac{e^x}{x+1}$
• B. $\dfrac{e^x}{(x+1)^3}$
• C. $\dfrac{x\cdot e^x}{(x+1)}$
• D. $\dfrac{e^x}{(x+1)^2}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Evaluate $\displaystyle\int _{ 0 }^{ \pi }{ \dfrac { x\sin ^{ 3 }{ x } }{ 1+\cos ^{ 2 }{ x } } dx }$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the definite integral:
$\displaystyle\int_{0}^{\pi/2}\dfrac{\cos^{2}x}{1+3\sin^{2}x}\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \int\sqrt{x}.\log xdx=$
• A. $\displaystyle \frac{2}{3}x^{3/2}.\log x+x^{3/2}+c$
• B. $x^{3/2}.(\displaystyle \log x-\frac{2}{3})+c$
• C. $\displaystyle \frac{2}{5}x^{3/2}(\log x+1)+c$
• D. $\displaystyle \frac{2}{3}x^{3/2}.\log x-\frac{4}{9}x^{3/2}+c$