Question Text
Question 1 :
If $\int { \left[ \log { \left( \log { x } \right) } +\cfrac { 1 }{ { \left( \log { x } \right) }^{ 2 } } \right] } dx=x\left[ f(x)-g(x) \right] +c$ then<br><br>
Question 3 :
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
Question 6 :
$\displaystyle\int { \sin ^{ -1 }{ \sqrt { \dfrac { x }{ a+x } } } dx } $ is equal to
Question 7 :
$\int { { ({ x }^{ 2 }+5) }^{ 3 } } dx$
Question 8 :
If $f\left( \cfrac { 3x-4 }{ 3x+4 } \right) =x+2$, then $\int { f(x) } dx$ is
Question 9 :
If $I =\displaystyle \int {\dfrac{{dx}}{{{{\left( {2ax + {x^2}} \right)}^{\frac{3}{2}}}}}} $, then $I$ is equal to