Mathematics

Evaluate
$$\int \dfrac {x+2}{2X^{2}+6x+5}dx$$


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Subjective Medium Published on 17th 09, 2020
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Realted Questions

Q1 TRUE/FALSE Medium
$$\int \sqrt {x^2 + a^2} dx =\dfrac{x}{2} \sqrt {x^2 + a^2} + \dfrac{a^2}{2} log (x +\sqrt {x^2 + a^2)} +c$$
  • A. False
  • B. True

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Hard
$$\displaystyle\int{\frac{(1+x^2)dx}{(1-x^2)\sqrt{1+x^2+x^4}}} = $$
  • A. $$\displaystyle I=-\frac{1}{2\sqrt{3}}\log{\left|\frac{\sqrt{x^2+\displaystyle\frac{1}{x^2}+1}-\sqrt{5}}{\sqrt{x^2+\displaystyle\frac{1}{x^2}+1}+\sqrt{5}}\right|}+C$$
  • B. $$\displaystyle I=-\frac{1}{4\sqrt{3}}\log{\left|\frac{\sqrt{x^2+\displaystyle\frac{1}{x^2}+1}-\sqrt{3}}{\sqrt{2x^2+\displaystyle\frac{1}{x^2}+1}+\sqrt{3}}\right|}+C$$
  • C. $$\displaystyle I=-\frac{1}{2\sqrt{3}}\log{\left|\frac{\sqrt{2x^2+\displaystyle\frac{1}{2x^2}+1}-\sqrt{3}}{\sqrt{2x^2+\displaystyle\frac{1}{2x^2}+1}+\sqrt{3}}\right|}+C$$
  • D. $$\displaystyle I=-\frac{1}{2\sqrt{3}}\log{\left|\frac{\sqrt{x^2+\displaystyle\frac{1}{x^2}+1}-\sqrt{3}}{\sqrt{x^2+\displaystyle\frac{1}{x^2}+1}+\sqrt{3}}\right|}+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Medium
Evaluate the given integral.
$$\displaystyle \int { { e }^{ x } } \left( \tan ^{ -1 }{ x } +\cfrac { 1 }{ 1+{ x }^{ 2 } }  \right) dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Medium
Solve:
$$\int { \dfrac { dx }{ 2{ x }^{ 2 }+x-1 }  } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Subjective Easy
Evaluate:
$$ \int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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