Mathematics

# If $\int\dfrac{1}{x\sqrt{1 - x^3}}dx = a \,log \left|\dfrac{\sqrt{1 - x^3}- 1}{\sqrt{1 - x^2}+ 1}\right| + b$ then $a =$

$\dfrac{1}{3}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

#### Realted Questions

Q1 Single Correct Medium
Solve $\int {\left[ {\log \,\left( {logx} \right) + \dfrac{1}{{{{\left( {\log x} \right)}}}}} \right]dx}$
• A. $I=4x\log \left( \log x \right)+C$
• B. $I=\log \left( \log x \right)+C$
• C. None of these
• D. $I=x\log \left( \log x \right)+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate: $\int \sqrt{1+sinx}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int \frac{x}{x^{2}+x+1}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Evaluate : $\int \dfrac { sec x}{( sec x + tan x ) } dx$
• A. $tan x+ sec x+ C$
• B. $-tan x + sec x + C$
• C. $-tan x - sec x + C$
• D. $tan x -sec x + C$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int { (\cfrac { { 2 }^{ x }-5^{ x } }{ 10^{ x } } )dx }$ is equal to __________________.
• A. $\cfrac { { 2 }^{ x } }{ \log _{ e }{ 2 } } -\cfrac { 5^{ x } }{ \log _{ e }{ 5 } } +c$
• B. $\cfrac { { 2 }^{ x } }{ \log _{ e }{ 2 } } +\cfrac { 5^{ x } }{ \log _{ e }{ 5 } } +c$
• C. $\cfrac { { 5 }^{ -x } }{ \log _{ e }{ 5 } } -\cfrac { 2^{ -x } }{ \log _{ e }{ 2 } } +c$
• D. $\cfrac { { 2 }^{ -x } }{ \log _{ e }{ 2 } } -\cfrac { 5^{ -x } }{ \log _{ e }{ 5 } } +c$