Mathematics

Evaluate : $$\displaystyle \int \dfrac{x}{x^{4}+x^{2}+1}\ dx$$


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Subjective Medium Published on 17th 09, 2020
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Q1 Single Correct Medium
$$\displaystyle \int\frac{\sec^{2}x}{5+4\tan x}dx=$$
  • A. $$\displaystyle \log|5+4\tan x|+c$$
  • B. $$\displaystyle -\frac{1}{5+4\tan x}+c$$
  • C. $$ \displaystyle- \frac{1}{4}\log|5+4\tan x|+c$$
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Q2 Subjective Medium
Evaluate: $$\int\limits_0^{\dfrac{\pi }{2}} {\cos x\;{e^{\sin x}}\;{\text{dx}}} $$

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Q3 Single Correct Medium
$$\displaystyle \int { \dfrac { { e }^{ 5\log { x }  }-{ e }^{ 4\log { x }  } }{ { e }^{ 3\log { x }  }-{ e }^{ 2\log { x }  } }  } dx=\_ \_ \_ \_ \_ \_ +c$$
  • A. $$e.{ 3 }^{ -3x }$$
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1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Medium
$$\displaystyle \int^{\pi/2n}_{0}\dfrac {dx}{1+(\tan nx)^{n}}$$ is equal to $$n\ \in\ N$$ 
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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 :

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1 Verified Answer | Published on 17th 08, 2020

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