Mathematics

# Evaluate:$\int { \cfrac { 8 }{ (x+2)({ x }^{ 2 }+4) } dx }$

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Subjective Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

#### Realted Questions

Q1 Subjective Medium
Integrate the rational function   $\cfrac {1}{x(x^4-1)}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\displaystyle\int { \cfrac { 1 }{ (x+2)({ x }^{ 2 }+1) } } dx=a\log { \left| 1+{ x }^{ 2 } \right| } +b\tan ^{ -1 }{ x } +\cfrac { 1 }{ 5 } \log { \left| x+2 \right| } +C$
• A. $a=-\cfrac { 1 }{ 10 } b=-\cfrac { 2 }{ 5 }$
• B. $a=\cfrac { 1 }{ 10 } b=-\cfrac { 2 }{ 5 }$
• C. $a=\cfrac { 1 }{ 10 } b=\cfrac { 2 }{ 5 }$
• D. $a=-\cfrac { 1 }{ 10 } b=\cfrac { 2 }{ 5 }$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\int \sqrt{\dfrac{cos x-cos^{3} x}{1-cos^{3} x}}$.dx is equal to

• A. $\dfrac{2}{3}sin^{-1}(cos^{3/2}x)+C$
• B. $\dfrac{3}{2}sin^{-1}(cos^{3/2}x)+C$
• C. none of these
• D. $\dfrac{2}{3}cos^{-1}(cos^{3/2}x)+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard

Evaluate: $\int \dfrac{\ cosx}{(1+\ sinx)(2 + \ sinx)} dx =$

• A. $log[(1 + \ sinx)(2 +\ sinx)] +c$
• B. $log \dfrac{2+\ sinx}{2+\ sinx} + c$
• C.  None of these
• D. $log \dfrac{1+\ sinx}{2+\ sinx} + c$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
If $\int { f(x)dx } =g(x)$, then $\int { { f }^{ -1 }(x) } dx$ is
[Where $C$ is constant of integration]
• A. $x{ f }^{ -1 }(x)+C$
• B. $f\left( { g }^{ -1 }(x) \right) +C$
• C. ${ g }^{ -1 }(x)+C$
• D. $x{ f }^{ -1 }(x)-g\left( { f }^{ -1 }(x) \right) +C$