Question Text
Question 5 :
For $x^{2} \neq n\pi + 1, n\epsilon N$ (the set of natural numbers), the integral<br>$\int x \sqrt {\dfrac {2\sin (x^{2} - 1) - \sin 2(x^{2} - 1)}{2\sin (x^{2} - 1) + \sin 2 (x^{2} - 1)}} dx$ is equal to<br>(where $c$ is a constant of integration).
Question 12 :
If $\displaystyle \int f(x)dx =2\{f(x)\}^{3}+c {\it}$,  and $f(x) \neq 0$   then $f(x)$ is<br/>
Question 13 :
The value of $\int \dfrac { d x } { x \sqrt { 1 - x ^ { 3 } } }$ is equal to
Question 14 :
If $\int \frac{x\, cos\,  \alpha+1 }{(x^2+2x\, cos\,  \alpha+1)^{3/2}}$ $dx= \frac{x}{\sqrt{f(x) + g(x)cos\, \alpha }}+c$ then (more than one option is correct)<br/>
Question 15 :
$\displaystyle\int { \dfrac { dx }{ x+\sqrt { x } } } $ is equal to
Question 17 :
$\int { \cfrac { 1 }{ 8\sin ^{ 2 }{ x } +1 } } dx$ is equal to
Question 18 :
Let $f$ be a function which is continuous and differentiable for all real $x$. If $f\left( 2 \right) = -4$ and $f^{ \prime }\left( x \right) \ge 6$ for all $x\in \left[ 2,4 \right] $, then
