Mathematics

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


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Subjective Hard Published on 17th 09, 2020
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Realted Questions

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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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. $$a=-\cfrac { 1 }{ 10 } b=\cfrac { 2 }{ 5 } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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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. $$\dfrac{2}{3}cos^{-1}(cos^{3/2}x)+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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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. $$ log \dfrac{1+\ sinx}{2+\ sinx} + c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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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. $$x{ f }^{ -1 }(x)-g\left( { f }^{ -1 }(x) \right) +C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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