Mathematics

# $\displaystyle\int _ { 0 } ^ { \pi } \dfrac { x \sin x } { 1 + \cos ^ { 2 } x } d x =$

$\frac { \pi ^ { 2 } } { 4 }$

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

#### Realted Questions

Q1 Single Correct Medium

$a_{k}=\displaystyle \frac{1}{k(k+1)}$ for  $k=1,2,3,\displaystyle \ldots n then(\sum_{k=1}^{n}a_{k})^{2}$
• A. $\displaystyle \frac{n}{n-1}$
• B. $\displaystyle \frac{n^{6}}{(n+1)^{6}}$
• C. $\displaystyle \frac{n^{4}}{(n-1)^{4}}$
• D. $\displaystyle \frac{n^{2}}{(n+1)^{2}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int \frac{3x+4}{x^{2}+4x+2}dx.$
• A. $\displaystyle \frac{3}{2}\log \left ( x^{2}+4x+2 \right )+\frac{1}{\sqrt{\left ( 2 \right )}}\log \frac{x+2-\sqrt{2}}{x+2+\sqrt{\left ( 2 \right )}}.$
• B. $\displaystyle \frac{3}{2}\log \left ( x^{2}+4x+2 \right )-\frac{1}{2\sqrt{\left ( 2 \right )}}\log \frac{x+2-\sqrt{2}}{x+2+\sqrt{\left ( 2 \right )}}.$
• C. $\displaystyle \frac{3}{2}\log \left ( x^{2}+4x+2 \right )-\frac{1}{\sqrt{2\left ( 2 \right )}}\log \frac{x+2-2\sqrt{2}}{x+2+\sqrt{\left ( 2 \right )}}.$
• D. $\displaystyle \frac{3}{2}\log \left ( x^{2}+4x+2 \right )-\frac{1}{\sqrt{\left ( 2 \right )}}\log \frac{x+2-\sqrt{2}}{x+2+\sqrt{\left ( 2 \right )}}.$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Integrate the rational function   $\displaystyle \frac {\cos x}{(1-\sin x)(2-\sin x)}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate $\displaystyle \int {\frac{{dx}}{{x + 4 - {x^2}}}}$

$\int { \dfrac { 3x }{ 3x-1 } dx }$