Question 3 :
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 5 :
What is $\displaystyle \int \dfrac{dx}{x(1 + ln x)^n}$ equal to $(n \neq 1)$ ?

Question 7 :
$\int { \sqrt { secx-1 } } dx$ is equal to

Question 11 :
$\displaystyle \int \dfrac {3^{x}}{\sqrt {1 - 9^{x}}} dx$ is equal to

Question 12 :
$\displaystyle\int { \dfrac { dx }{ x+\sqrt { x } } } $ equals

Question 17 :
$f(x), g(x)$ are two differentiable function on $[0, 2]$ such that ${f}''\left ( x \right )-{g}''\left ( x \right )=0$ and ${f}'\left ( 1 \right )=4=2{g}'\left ( 1 \right )$ and $f\left ( 2 \right )=3g\left ( 2 \right )=9$ then $\left [ f\left ( x \right )-g\left ( x \right ) \right ]$ at $\displaystyle x=\dfrac{3}{2}$ is<br>

Question 18 :
$\displaystyle \int { \dfrac { \left( x+2 \right) dx }{ \sqrt { \left( x-2 \right) \left( x-3 \right)&#160; }&#160; }&#160; }$ is equal to:

Question 19 :
$\int {{e^x}(\log \sin x + \cot x)\,dx = } \_\_\_\_\_\_ + C.$

Question 25 :
If $\displaystyle \int \dfrac{dx}{\sqrt{\sin^3 x \cos^5 x}} = a \sqrt{\cot x } + b \sqrt {\tan^3x} + c$ where c is an arbitrary constant of integration then the values of $'a'$ and $'b'$ are respectively :<br/>