Question Text
Question 3 :
If $\displaystyle l^{r}(x)$ means $\log \log \log .........x,$ the $\log $ being repeated r times, then$\displaystyle \int \left [x l(x)l^{2}(x)l^{3}(x)......l^{r}(x) \right ]^{-1}dx$is equal to<br>
Question 5 :
$\displaystyle \int { \frac { \sqrt { x }  }{ \sqrt { { x }^{ 3 }+4 }  } dx } $ is equal to
Question 6 :
$\int { \cfrac { 1 }{ 8\sin ^{ 2 }{ x } +1 } } dx$ is equal to
Question 7 :
Evaluate: $\displaystyle \int { \dfrac { x\sqrt { x } .dx }{ \sqrt { 1-{ x }^{ 5 } }  } } $
Question 8 :
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 9 :
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 10 :
$\int \dfrac{cos 2x - cos 2 \theta}{cos x - cos \theta} dx$ is equal to