Mathematics

# $\displaystyle\int \cos \left[2\cot^{-1}\sqrt{\dfrac{1-x}{1+x}}\right]dx$ is equal to?

##### ANSWER

$\dfrac{1}{2}x^2+c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Assertion & Reason Hard
##### ASSERTION

STATEMENT-1 : $\displaystyle \int \frac{\left \{ f(x)\phi '(x)-f'(x)\phi (x) \right \}}{f(x)\phi (x)}\left \{ \log \phi (x)-\log f(x) \right \}dx=\frac{1}{2}\left \{ \log \frac{\phi(x)}{f(x)} \right \}^{2}+c$

##### REASON

STATEMENT-2 : $\displaystyle \int (h(x))^{n}h'(x)dx=\frac{(h(x))^{n+1}}{n+1}+c$

• A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
• B. STATEMENT-1 is True, STATEMENT-2 is False
• C. STATEMENT-1 is False, STATEMENT-2 is True
• D. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If $\dfrac{3x^{2}+10x+13}{(x-1)^{4}}=\dfrac{A}{(x-1)^{2}}+\dfrac{B}{(x-1)^{3}}+\dfrac{C}{(x-1)^{4}}$ then descending order of $A,B,C$
• A. $A, B, C$
• B. $A, C, B$
• C. $C, A, B$
• D. $C, B, A$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle\int \displaystyle\frac{\cos \alpha}{\sin x\cos (x-\alpha)}dx=$___________ $+$c where $0 < x < \alpha < \pi_{/2}$ and $\alpha$-constant.
• A. $-ln|tan x+\cot \alpha|$
• B. $ln|\cot x+\tan\alpha|$
• C. $ln|tan x+\cot \alpha|$
• D. $-ln|\cot x+\tan\alpha|$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate: $\int { \cfrac { x+3 }{ \left( x-1 \right) \left( { x }^{ 2 }+1 \right) } } dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

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