Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
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Realted Questions

Q1 Single Correct Medium
$$\displaystyle \int\frac{e^{x}}{e^{2x}+5e^{x}+6}dx=$$
  • A. $$\displaystyle \log|\frac{e^{x}+3}{e^{x}+2}|+c$$
  • B. $$\displaystyle \log|\frac{e^{x}-2}{e^{x}-3}|+c$$
  • C. $$\displaystyle \log|\frac{e^{x}-3}{e^{x}-2}|+c$$
  • D. $$\displaystyle \log|\frac{e^{x}+2}{e^{x}+3}|+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Subjective Hard
$$\displaystyle \int { \sqrt { \sin { x }  }  } $$dx

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Medium
Prove that $$\displaystyle\int^{\infty}_0\dfrac{x}{(1+x)(1+x^2)}dx=\dfrac{\pi}{4}$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Medium
$$\displaystyle \int \dfrac {dx}{\sqrt {x}(x+9)}$$ is equal to, $$(x > 0)$$
  • A. $$\dfrac {2}{5}\tan^{-1}(\sqrt {x})+c$$
  • B. $$\tan^{-1}(\sqrt {x})+c$$
  • C. $$\tan^{-1}\left(\dfrac {\sqrt {x}}{3}\right)+c$$
  • D. $$\dfrac {2}{3}\tan^{-1}\left(\dfrac {\sqrt {x}}{3}\right)+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Passage Medium
Consider two differentiable functions $$f(x), g(x)$$ satisfying $$\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$$ & $$\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$$. where $$\displaystyle f(x)>0    \forall  x \in  R$$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives


1 Verified Answer | Published on 17th 08, 2020

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