Mathematics

# Find proper substitution$\int _{ 0 }^{ 1 }{ \dfrac { { e }^{ -x } }{ 1+{ e }^{ -x } } dx }$

$1+{ e }^{ -x }\rightarrow t$

##### SOLUTION
$\int _{ 0 }^{ 1 }{ \cfrac { { e }^{ -x } }{ 1+{ e }^{ -x } } dx }$
$1+{ e }^{ -x }=t$
$\Rightarrow { -e }^{ -x }dx=dt$
$\int _{ 0 }^{ 1 }{ \cfrac { -dt }{ t } } \quad \therefore 1+{ e }^{ -x }=t$

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
$\int { \cfrac { f'(x) }{ f(x) } dx } =\log { [f(x)] } +c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\displaystyle \int \frac{dx}{\left ( x-p \right )\sqrt{\left ( x-p \right )\left ( x-q \right )}} \displaystyle =-\frac{2}{p-q}\sqrt{\frac{x-a}{x-b}}+c$ then find $a$ and $b$ are respectively
• A. $p,q$
• B. $q,q^2$
• C. $p^2,q^2$
• D. $q,p$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate: $\displaystyle\int {{sin^{ - 1}}} \left( {{{2x} \over {1 + {x^2}}}} \right)dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Evaluate $\displaystyle\int^{3}_{2}3^{x}dx$
• A. $\dfrac{1}{\ln 3}$
• B. $\dfrac{8}{\ln 3}$
• C. None of these
• D. $\dfrac{18}{\ln 3}$

Solve : $\displaystyle \int \dfrac{x^2 + x + 5}{3x + 2} dx$