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 $$a =$$


ANSWER

$$\dfrac{1}{3}$$


SOLUTION
View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114
Enroll Now For FREE

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. $$ I=x\log \left( \log x \right)+C $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$ tan x -sec x + C $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$\cfrac { { 2 }^{ -x } }{ \log _{ e }{ 2 } } -\cfrac { 5^{ -x } }{ \log _{ e }{ 5 } } +c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer