Mathematics

# The value of $\overset { 1 }{ \underset { 0 }{ \int} } \dfrac{8log(1+x)}{1+x^2}dx$ is:-

$\dfrac{\pi}{2}log2$

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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
Let $\displaystyle f\left ( x \right )=\int \frac{x^{2}dx}{\left ( 1+x^{2} \right )\left ( 1+\sqrt{1+x^{2}} \right )}$ and $\displaystyle f\left ( 0 \right )=0.$ Then $\displaystyle f\left ( 1 \right )$ is
• A. $\displaystyle \log \left ( 1+\sqrt{2} \right )$
• B. $\displaystyle \log \left ( 1+\sqrt{2} \right )+\frac{\pi }{4}$
• C. none of these
• D. $\displaystyle \log \left ( 1+\sqrt{2} \right )-\frac{\pi }{4}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $M= \displaystyle \int _{ 0 }^{ \pi /2 }{ \cfrac { \cos { x } }{ x+2 } } dx,N=\int _{ 0 }^{ \pi /4 }{ \cfrac { \sin { x } \cos { x } }{ { \left( x+1 \right) }^{ 2 } } } dx\quad$, then the value of $M-N$ is ?
• A. $\pi$
• B. $\cfrac { \pi }{ 4 }$
• C. $\cfrac { 2 }{ \pi -4 }$
• D. $\cfrac { 2 }{ \pi +4 }$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\displaystyle \int 16x\sec ^2(2x^2+1) dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Find: $\displaystyle \int \dfrac{e^x dx}{(e^x - 1)^2 (e^x + 2)}$

1 Verified Answer | Published on 17th 09, 2020

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