Mathematics

# If $\displaystyle\int\frac{(x-1)^2}{x^4+x^2+1}dx=f(x)+C,$ then the value of $\lim_\limits{x \to \infty}f(x)$ is equal to

$\frac{-\pi}{2\sqrt3}$

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

#### Realted Questions

Q1 Subjective Medium
$Evalute\;\int {\dfrac{{\cot x}}{{\sqrt {\sin x} }}} dx.$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Let $I_1=\displaystyle\int^1_0\dfrac{e^xdx}{1+x}$ and $I_2=\displaystyle\int^1_0\dfrac{x^2dx}{e^{x^3}(2-x^3)}$, then $\dfrac{I_1}{I_2}$ is?
• A. $e/3$
• B. $3e$
• C. None of these
• D. $3/e$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\int _0^1 xdx = \dfrac {\pi}{4} - \dfrac {1}{2} ln 2$ then the value of definite integral $\int _0^1 \tan^{-1} (1-x+x^2) dx$ equals :
• A. $\dfrac {\pi}{4} + ln 2$
• B. $\dfrac {\pi}{4} - ln2$
• C. $2 ln 2$
• D. $ln2$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate: $\sqrt {\left( {1 + \sin 2x} \right)}$ with respect to $x$.

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
$\displaystyle \int_{1}^{e^{37}}\frac{\pi \sin \left ( \pi \log _{e}x \right )}{x}dx$ is equal to
• A. $\displaystyle -2$
• B. $\displaystyle 2/\pi$
• C. $\displaystyle 2\pi$
• D. $2$