Mathematics

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

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

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. $\displaystyle- \frac{1}{4}\log|5+4\tan x|+c$
• D. $\displaystyle {\frac{1}{4}}\log|5+4\tan x|+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate: $\int\limits_0^{\dfrac{\pi }{2}} {\cos x\;{e^{\sin x}}\;{\text{dx}}}$

1 Verified Answer | Published on 17th 09, 2020

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. $e.{ 3 }^{ -3x }$
• B. ${ e }^{ 3 }\log { x }$
• C. $\dfrac{{ x }^{ 2 }} 3$
• D. $\dfrac{{ x }^{ 3 }} 3$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int^{\pi/2n}_{0}\dfrac {dx}{1+(\tan nx)^{n}}$ is equal to $n\ \in\ N$
• A. $\dfrac {n\pi}{4}$
• B. $\dfrac {\pi}{2n}$
• C. $\dfrac {2\pi}{n}$
• D. $\dfrac {\pi}{4n}$

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 $\displaystyle f(x)>0 \forall x \in R$