Mathematics

# If $\displaystyle \int { \frac { { e }^{ x }-1 }{ { e }^{ x }+1 } dx } =f\left( x \right) +C$, then $f\left( x \right)$ is equal to

$2\log { \left( { e }^{ x }+1 \right) }$

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

#### Realted Questions

Q1 Single Correct Medium
If $f(x)=\int { \cfrac { dx }{ \sin ^{ 1/2 }{ x } \sin ^{ 7/2 }{ x } } }$, then $f(\cfrac{\pi}{4})-f(0)=$
• A. $2.3$
• B. $2.4$
• C. $2.5$
• D. $2.67$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Solve $\displaystyle\int \dfrac {1}{\tan x+\cos x+\sec x+\csc x}dx.$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\int \dfrac{(\log x)^2}{x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
If $\displaystyle \int \dfrac{dx}{x^3(1+x^6)^{2/3}} = xf(x) (1 + x^6)^{\frac{1}{3}} + C$
where $C$ is a constant of integration, then the function $f(x)$ is equal to -
• A. $-\dfrac{1}{6x^3}$
• B. $\dfrac{3}{x^2}$
• C. $-\dfrac{1}{2x^2}$
• D. $-\dfrac{1}{2x^3}$

If $y=2^23^{2x}5^{-5}7^{-5}$ then $\dfrac{dy}{dx}=$