Mathematics

Evaluate the following :$\displaystyle \int{\left(\dfrac{\tfrac{x}{x+1}-ln(x+1) }{x(ln(x+1)) }\right)}dx$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

Realted Questions

Q1 Single Correct Hard
Evaluate $\displaystyle\int{\frac{dx}{\sqrt{(x-a)(b-x)}}}$.
• A. $\displaystyle I=2\cos^{-1}{\sqrt{\frac{x-a}{(b-a)}}}+C$
• B. $\displaystyle I=\sin^{-1}{\sqrt{\frac{x-a}{(b-a)}}}+C$
• C. $\displaystyle I=2\sin^{-1}{\sqrt{\frac{x-b}{(a-b)}}}+C$
• D. $\displaystyle I=2\sin^{-1}{\sqrt{\frac{x-a}{(b-a)}}}+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\int _{0}^{-\pi/2} \ln (\sin^{2}{\theta}+k^{2}\cos^{2}{\theta})d\theta$ is equal to
• A. $\dfrac{\pi}{2} \ \ln ({k+1})$
• B. ${\pi} \ \ln ({k+1})$
• C. $\dfrac{\pi}{2} \ \ln ({\dfrac{k+1}{2}})$
• D. $\pi \ \ln ({\dfrac{k+1}{2}})$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $\displaystyle\int { \cfrac { 1 }{ 5+4\sin { x } } } dx=A\tan ^{ -1 }{ \left( B\tan { \cfrac { x }{ 2 } } +\cfrac { 4 }{ 3 } \right) } +C\quad$, then
• A. $A=\cfrac { 1 }{ 3 } ,B=\cfrac { 2 }{ 3 }$
• B. $A=-\cfrac { 2 }{ 3 } ,B=\cfrac { 5 }{ 3 }$
• C. $A=\cfrac { 1 }{ 3 } ,B=-\cfrac { 5 }{ 3 }$
• D. $A=\cfrac { 2 }{ 3 } ,B=\cfrac { 5 }{ 3 }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the integrals:
$\displaystyle \int \dfrac{4x}{(2x^2+3)}dx$

$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$