Mathematics

# Evaluate $\displaystyle \int \frac{e^{-x}}{1+e^{x}}dx$

$log(1+e^{x})-x-e^{-x}+c$

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

#### Realted Questions

Q1 Single Correct Hard
The value of $\displaystyle \int_{-1/2}^{1/2} \ cosx \ ln(x+\sqrt{1+x^2})dx$ is equal to ?
• A. $1$
• B. $-In2$
• C. $\sqrt{2}+In2$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
Solve:
$\int_{\dfrac{\pi}{2}}^ {\dfrac{\pi}{2}}tanx^{3}\ dx=$
• A. $1$
• B. $\dfrac{1}{2}$
• C. $2$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Solve: $\int _ { 0 } ^ { \pi } \left( x \cdot \sin ^ { 2 } x \cdot \cos x \right) d x =$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Evaluate the following integrals:$\displaystyle \int \sqrt{4-9x^{2}}dx$
• A. $\dfrac{x}{2}.\sqrt{4-9x^{2}}+\dfrac12 \sin^{-1}\left ( \dfrac{3x}{2} \right )+C$
• B. $\dfrac{x}{2}.\sqrt{4-9x^{2}}+ \sin^{-1}\left ( \dfrac{3x}{2} \right )+C$
• C. none of these
• D. $\dfrac{x}{2}.\sqrt{4-9x^{2}}+\dfrac23 \sin^{-1}\left ( \dfrac{3x}{2} \right )+C$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
Let $f:R \to R,g:R \to R$ be continuous functions. Then the value of indtegral
$\displaystyle \int\limits_{In\lambda }^{InI/\lambda } {\frac{{f\left( {\dfrac{{{x^2}}}{4}} \right)\left[ {f\left( x \right) - f\left( { - x} \right)} \right]}}{{g\left( {\dfrac{{{x^2}}}{4}} \right)\left[ {g\left( x \right) + g\left( { - x} \right)} \right]}}} dx$

• A. a non-zero constant
• B. Zero
• C. None of these
• D. depend on $\lambda$