Mathematics

# Evaluate : $\displaystyle \int \dfrac{x}{x-\sqrt{x^2-1}}dx$

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

#### Realted Questions

Q1 Single Correct Hard
Evaluate $\displaystyle \int_{-\pi /2}^{\pi /2}\left \{ \log \left(\frac{px^{2}+qx+r}{px^{2}-qx+r}\cdot \left ( a+b \right )\cdot \left | \sin x \right | \right) \right \}dx$
• A. $\displaystyle -\pi \log \left ( \frac{a+b}{2} \right ).$
• B. $\displaystyle \frac{\pi}{2} \log \left ( (a+b) \right ).$
• C. $\displaystyle \pi \log \left ( \frac{a+b}{4} \right ).$
• D. $\displaystyle \pi \log \left ( \frac{a+b}{2} \right ).$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\displaystyle \int\frac{\sqrt[2]{x}}{1+\sqrt[4]{x^{3}}}dx$ is equal to
• A. $\displaystyle \frac{4}{3}[1+x^{3/4}+\log(1+x^{3/4})]+c$
• B. $\displaystyle \frac{4}{3}[1-x^{3/4}+\log(1+x^{3/4})]+c$
• C. $\displaystyle \frac{4}{3}[1-x^{3/4}-\log(1+x^{3/4})]+c$
• D. $\displaystyle \frac{4}{3}[1+x^{3/4}-\log(1+x^{3/4})]+c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle \int _ { 0 } ^ { \pi / 4 } \frac { x \cdot \sin x } { \cos ^ { 3 } x } d x$ equals to :
• A. $\displaystyle \frac { \pi } { 4 } + \frac { 1 } { 2 }$
• B. $\dfrac { \pi } { 4 }$
• C. $\dfrac { \pi } { 4 } + 1$
• D. $\displaystyle \frac { \pi } { 4 } - \frac { 1 } { 2 }$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of intergral$\int_{\pi \4}^{3\\pi }\frac{x}{1+4x}$
• A.
• B.
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• D.

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