Mathematics

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

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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
$\int \dfrac{x}{\sqrt{x^2+2}}dx$
• A. $\dfrac{x^2+2}{2}+C$
• B. $x^2+2+C$
• C. $\dfrac{1}{2}\sqrt{x^2+2}+C$
• D. $\sqrt{x^2+2}+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If f(x) be an increasing function defined on [a, b] then
max {f(t) such that $a\leq t\leq x$, $a\leq x\leq b$}=f(x)  & min {f(t), $a\leq t\leq x$, $a\leq x\leq b$}=f(a) and if f(x) be decreasing function defined on [a, b] then
max {f(t), $a\leq t\leq x$, $a\leq x\leq b$}=f(a),
min {f(t), $a\leq t\leq x$, $a\leq x\leq b$}=f(x).
On the basis of above information answer the following questions.

Let $f\left ( x \right )=min. \left \{ \left | x \right |, \left | x-1 \right |, \left | x+1 \right | \right \}$ then $\int_{-1}^{1}f\left ( x \right )dx$ equals
• A. $\displaystyle \frac{1}{4}$
• B. 1
• C. None of these
• D. $\displaystyle \frac{1}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
$I=\displaystyle \int x^{3}\log{x}\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate: $f(x)=\dfrac { \sin ^{ 3 }{ x } +\cos ^{ 3 }{ x } }{ \sin ^{ 2 }{ x } \cos ^{ 2 }{ x } }$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
The value of $\underset {n\rightarrow \infty}{\lim}\dfrac {1}{n}\displaystyle \sum_{r = 1}^{r = 2n} \dfrac {r}{\sqrt {n^{2} + r^{2}}}$ equals.
• A. $\sqrt {5} + 1$
• B. $1 = \sqrt {5}$
• C. None of these
• D. $\sqrt {5} - 1$