Mathematics

Solve - 
$$\int {\dfrac{{\cos x}}{{1 - \cos x}}} dx$$


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Subjective Medium Published on 17th 09, 2020
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Q1 Single Correct Medium
$$\displaystyle \int\frac{dx}{2-3\cos 2x}=$$
  • A. $$\displaystyle \frac{1}{\sqrt{5}}\log|\frac{\sqrt{5}tanx-1}{\sqrt{5}tanx+1}|+c$$
  • B. $$\displaystyle \frac{-1}{2\sqrt{5}}\log|\frac{\sqrt{5}tanx-1}{\sqrt{5}tanx+1}|+c$$
  • C. $$-\dfrac{1}{\sqrt{5}}\log|\displaystyle \frac{\sqrt{5}tanx-1}{\sqrt{5}tanx+1}|+c$$
  • D. $$\displaystyle \frac{1}{2\sqrt{5}}\log|\frac{\sqrt{5}tanx-1}{\sqrt{5}tanx+1}|+c$$

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1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
$$\int\dfrac{dx}{\sqrt{1-x^2}-1}=$$
  • A. $$\dfrac{1+\sqrt{1-x^2}}{x}-2tan^{-1}\sqrt{\dfrac{1+x}{1-x}}+C$$
  • B. $$\dfrac{1+\sqrt{1-x^2}}{x}+2tan^{-1}\sqrt{\dfrac{1+x}{1-x}}+C$$
  • C. $$\dfrac{1+\sqrt{1-x^2}}{x}+2tan^{-1}\sqrt{\dfrac{1-x}{1+x}}+C$$
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Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Medium
The value of $$\int  \sqrt { \dfrac { e^ x\quad -\quad 1 }{ e^ x\quad +\quad 1 }  } dx$$ is equal to
  • A. $$\ell n\left( e^ x+\sqrt { e^ 2x\quad -1 } \right) - sec^ -1(e^ x)+c$$
  • B. $$\ell n\left( e^ x+\sqrt { e^ 2x\quad -1 } \right) +sec^ -1(e^ x)+c$$
  • C. $$\ell n\left( e^ x-\sqrt { e^ 2x\quad -1 } \right) -sec^ -1(e^ x)+c$$
  • D. $$\ell n\left( e^ x+\sqrt { e^ 2x\quad -1 } \right) -sin^ -1(e^ {-x})+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Hard
Find solution in terms of indefinite integration, using substitution 
   $$\int_0^1 {x\cos \left( {{{\tan }^{ - 1}}x} \right)} \,dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Subjective Medium
$$\int { \cfrac { f'(x) }{ f(x) } dx } =\log { [f(x)] } +c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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