Mathematics

# $\displaystyle\int _{ -1 }^{ 1 }{ x\ell n\left( 1+{ e }^{ x } \right) dx } =$

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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 Hard
$\displaystyle \int_{-1}^{1} \cot^{-1} \left(\dfrac{x+x^{3}}{1+x^{4}}\right)dx$ is equal to
• A. $2\pi$
• B. $\dfrac{\pi}{2}$
• C. $\pi$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$ is equal to?
• A. $ln\left|\dfrac{x^3+1}{x^2}\right|+c$
• B. $\dfrac{1}{2}\ln\left|\dfrac{x^3+1}{x^2}\right|+c$
• C. $\dfrac{1}{2}ln\left|\dfrac{x^3+1}{x}\right|+c$
• D. $ln\left|\dfrac{x^3+1}{x}\right|+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve: $\displaystyle\int{\dfrac{\sin\sqrt x}{\sqrt x}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Multiple Correct Medium
$\displaystyle \int \frac{dx}{x^{3}\left ( 1 - \displaystyle \frac{1}{2x^{2}} \right )}$ equals
• A. $ln| 2x^{2} - 1| + 2\, ln |x| + C$
• B. $ln| 2x^{2} - 1| - 2\, ln |x| + C$
• C. $ln| 2x^{2} - 1| - ln (x^{2}) - ln2 + C$
• D. $ln \left | 1 - \displaystyle \frac{1}{2x^{2}} \right | + c$

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 $\displaystyle f(x)>0 \forall x \in R$