Mathematics

# $\int _{ 0 }^{ 1 }{ \cfrac { logx }{ \sqrt { 1-{ x }^{ 2 } } } } dx=$

$\cfrac { \pi }{ 2 } log2$

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

#### Realted Questions

Q1 Subjective Medium
Integrate $\displaystyle\int {\sqrt {\frac{{1 + x}}{{1 - x}}} dx\ , on ( - 1,1)\,.}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium

Evaluate the following definite integral:

$\displaystyle \int _{0}^{\pi /2} \cos^2 x\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \frac{1}{x^{4}+1}=$
• A. $[\displaystyle \frac{x+\sqrt{2}}{2\sqrt{2}\sqrt{2}}\frac{x+\sqrt{2}}{2\sqrt{2}(x^{2}-\sqrt{2}x+1)}]$
• B. $[\displaystyle \frac{x+\sqrt{2}}{x^{2}+\sqrt{2}x+1}-\frac{x+\sqrt{2}}{(x^{2}-\sqrt{2}x+1)}]$
• C. $[\displaystyle \frac{x+\sqrt{2}}{2\sqrt{2}(x^{2}+\sqrt{2}x+1)}\frac{\sqrt{2}-x}{(-\sqrt{2})}]$
• D. $\displaystyle \frac{1}{2\sqrt{2}}[\frac{\mathrm{x}+\sqrt{2}}{(\mathrm{x}^{2}+\sqrt{2}\mathrm{x}+1)}+\frac{\sqrt{2}-\mathrm{x}}{(\mathrm{x}^{2}-\sqrt{2}\mathrm{x}+1)}]$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium

$\displaystyle \overset{\infty}{\underset{0}{\int}} x^6 e^{\tfrac{-x}{2}} dx =$

• A. $2^6 \left \lfloor 6 \right.$
• B. $\dfrac{ \left \lfloor 6 \right.}{2^7}$
• C. $\dfrac{ \left \lfloor 6 \right.}{2^6}$
• D. $2^7 \left \lfloor 6 \right.$

Evaluate :  $\int e ^ { \sin ^ { - 1 } x } \left( \dfrac { \ell n x } { \sqrt { 1 - x ^ { 2 } } } + \dfrac { 1 } { x } \right) d x$