Mathematics

# The value of $\displaystyle\int _{ 0 }^{ \infty }{ \frac { \log { x } }{ { a }^{ 2 }+{ x }^{ 2 } } dx }$

$\dfrac{2\pi \log a}{a}$

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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 Hard
Solve:
$\displaystyle \int_{0}^{2\pi}{e^{x}.\sin\left(\dfrac{\pi}{4}+\dfrac{x}{2}\right)dx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\int{ e }^{ x }\dfrac { 1-\sin { x } }{ 1-\cos { x } } dx=f\left( x \right) +$ constant, then $f\left( x \right)$ is equal to
• A. ${ e }^{ x }\cot { \dfrac { x }{ 2 } } +c$
• B. ${ e }^{ -x }\cot { \dfrac { x }{ 2 } } +c$
• C. $-{ e }^{ -x }\cot { \dfrac { x }{ 2 } } +c$
• D. $-{ e }^{ x }\cot { \dfrac { x }{ 2 } } +c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Find the value of $\displaystyle\int _{ 0 }^{ 2\pi }{ \sin ^{ 2 }{ x } \cdot \cos ^{ 4 }{ x } dx }$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int\frac{sin^{2}x}{1-cosx}$ $dx=$
• A. $xsinx+c$
• B. $x-sinx+c$
• C. $x^{2}\sin x+c$
• D. $x+sinx+c$

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