Mathematics

# $\displaystyle \int { \frac { { x }^{ 2 } }{ { \left( 2+{ 3x }^{ 2 } \right) }^{ 5/2 } } dx }$ is equal to

$\dfrac { 1 }{ 5 } { \left[ \dfrac { { x }^{ 2 } }{ 2+3{ x }^{ 2 } } \right] }^{ 3/2 }+C$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Subjective Medium
$-2 \int x^2 e^{-2x} dx = e^{-2x} (ax^2 + bx + c) + d$, then

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int \frac{\sqrt{2+x^{10}}}{x^{16}}dx$
• A. $\displaystyle \frac { 1 }{ 30 } \times { (\frac { 2 }{ { x }^{ 10 } } +1) }^{ \dfrac { 3 }{ 2 } }$
• B. $\displaystyle { (\frac { 2 }{ { x }^{ 30 } } +1) }^{ \dfrac { 3 }{ 2 } }$
• C. $\displaystyle \frac { 1 }{ 30 } \times { (\frac { 2 }{ { x }^{ 10 } } +1) }^{ \dfrac { 1 }{ 2 } }$
• D. $\displaystyle -\frac { 1 }{ 30 } \times { (\frac { 2 }{ { x }^{ 10 } } +1) }^{ \dfrac { 3 }{ 2 } }$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $f(x) = \dfrac {x + 2}{2x + 3}$, then $\displaystyle \int \left (\dfrac {f(x)}{x^{2}}\right )^{1/2} dx = \dfrac {1}{\sqrt {2}}g \left (\dfrac {1 + \sqrt {2f(x)}}{1 - \sqrt {2f(x)}}\right ) - \sqrt {\dfrac {2}{3}}h \left (\dfrac {\sqrt {3f(x)} + \sqrt {2}}{\sqrt {3f(x)} - \sqrt {2}}\right ) + c$, where
• A. $g(x) = \log |x|, h(x) = \tan^{-1}x$
• B. $g(x) = h(x) = \tan^{-1}x$
• C. $g(x) = \log|x|, h(x) = \log |x|$
• D. $g(x) = \tan^{-1} x, h(x) = \log |x|$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following:
$\displaystyle \int_{0}^{\frac{\pi}{2}} \dfrac{tan \,xdx}{1 + m^2 \,tan^2 x}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \int _{ 0 }^{ 1 }{ \tan ^{ -1 }{ \left( \dfrac { 2x }{ 1-{ x }^{ 2 } } \right) dx } } =\dfrac{\pi}{a}-\ln a$. Find $a$.
• A. $1$
• B. $-1$
• C. None of these
• D. $2$