Mathematics

# solve $\displaystyle\int\dfrac { e^{ 2x }-{ e }^{ -2x } }{ { e }^{ 2x }+{ e }^{ -2c } }dx$

##### SOLUTION
$\displaystyle\int\dfrac { e^{ 2x }-{ e }^{ -2x } }{ { e }^{ 2x }+{ e }^{ -2c } }dx$

Put ,  $e^{2x} + e^{-2x} = t$
$\implies (e^{2x}(2) + e^{-2x}(- 2) ) dx = dt$

$\implies ( e^{2x} - e^{-2x}) dx = \dfrac{1}{2} dt$

Now, $\displaystyle\int \dfrac{e^{2x} - e^{-2x}}{e^{2x} + e^{-2x}} dx = \int \dfrac{1}{2t} dt$

$= \dfrac{1}{2} \log {t} + c$

$= \dfrac{1}{2} \log (e^{2x} + e^{-2x}) + c$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Hard
Evaluate:
$\int { \cfrac { { e }^{ x } }{ ({ e }^{ 3x }-3{ e }^{ 2x }-{ e }^{ x }+3) } dx }$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
$\int { \dfrac { \tan { 2\theta } }{ \sqrt { \cos ^{ 6 }{ \theta } +\sin ^{ 6 }{ \theta } } } d\theta }$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int \frac{ln(\frac{x-1}{x+1})}{x^{2}-1}dx$ is equal to

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate: $\displaystyle\int { \cfrac { \sin { x } +\cos { x } }{ \sqrt { 9+16\sin { 2x } } } } dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Easy
Evaluate:
$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020