Mathematics

# The value of $\int { \cfrac { dx }{ x\sqrt { 1-{ x }^{ 3 } } } }$ is equal to

$\dfrac13\ln { \left| \cfrac { \sqrt { 1-{ x }^{ 3 } } -1 }{ \sqrt { 1-{ x }^{ 3 } } +1 } \right| +C }$

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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 Medium
$\displaystyle \int {\cos 2\theta \,\log \left( {\frac{{\cos \theta + \sin \theta }}{{\cos \theta - \sin \theta }}} \right)} d\theta$ is equal to.
• A. ${(\cos \theta + \sin \theta )^2}\log \left( {\frac{{\cos \theta + \sin \theta }}{{\cos \theta - \sin \theta }}} \right) + C$
• B. $\frac{{{{(\cos \theta - \sin \theta )}^2}}}{2}\log \left( {\frac{{\cos \theta + \sin \theta }}{{\cos \theta - \sin \theta }}} \right) + C$
• C. None of these
• D. ${(\cos \theta - \sin \theta )^2}\log \left( {\frac{{\cos \theta + \sin \theta }}{{\cos \theta - \sin \theta }}} \right) + C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int_{0}^{\pi /2}\frac{dx}{\sin x}$equals
• A. $\displaystyle \frac{1}{2}$
• B. $1$
• C. $3/2$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\displaystyle \int \dfrac{1}{3x^{2}+x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int\frac{4\sec^{2}x\tan x}{\sec^{2}x+\tan^{2}x}dx=$
• A. $2\log(\sec^{2}x+\tan^{2}x)+c$
• B. $\log(2x+\tan^{2}x)+c$
• C. $2\tan^{2}x+c$
• D. $\log (\sec^{2}x+\tan^{2}x) +c$

$\int(2x^2-3 \, sin x+5 \sqrt{x})dx$