Question 3 :
What is $\displaystyle \int \dfrac{dx}{x(1 + ln x)^n}$ equal to $(n \neq 1)$ ?
Question 8 :
$\int { \sqrt { secx-1 } } dx$ is equal to
Question 9 :
The value of $\displaystyle\int \dfrac{\cos\ 2\ x}{\cos\ x}\ dx$ is equal to
Question 14 :
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 19 :
$\displaystyle\int { \dfrac { dx }{ x+\sqrt { x } } } $ equals
Question 22 :
$\int \dfrac {x^{2} - 1}{x^{4} + 3x^{2} + 1} dx (x > 0)$ is
Question 23 :
$\displaystyle \int \dfrac{1}{\sqrt{x}} \tan^4 \, \sqrt{x} \, \sec^2 \, \sqrt{x} \, dx = $
Question 24 :
If $\int \frac { x ^ { 2 } \tan ^ { - 1 } x } { 1 + x ^ { 2 } } d x = \tan ^ { - 1 } x - \frac { 1 } { 2 } \log \left( 1 + x ^ { 2 } \right) + f ( x ) + c$ then $f ( x ) =$
Question 25 :
Evaluate $\displaystyle \int_{}^{} {x\sqrt {\frac{{{a^2} - {x^2}}}{{{a^2} + {x^2}}}} dx  } $
Question 26 :
$\displaystyle \int \dfrac {\sin x + \cos x}{e^{-x} + \sin x} dx$ is equal to
Question 28 :
The anti derivative of $\displaystyle \left (\sqrt x+\frac {1}{\sqrt x}\right )$ equals<br>
Question 30 :
The value of $\displaystyle \int {\dfrac{{d({x^2} + 1)}}{{\sqrt {{x^2} + 2} }}} ,$ is 
Question 31 :
Assertion: If $D(x)\, =\,\begin{vmatrix} f_{1}(x) &  & f_{2}(x) &  & f_{3}(x) & \\ a_{2} &  & b_{2} &  & c_{2} & \\ <br/>a_{3} &  & b_{3} &  & c_{3} & \end{vmatrix}$ , where <br/>$f_{1}$,$f_{2}, f_{3}$ are differentiable function and $a_{2},\, b_{2},\, c_{2},\,<br/>a_{3},\, b_{3},\, c_{3}$ are constants then $\int D(x)dx\,=\, \begin{vmatrix}\int f_{1}(x)dx &  & \int f_{2}(x)dx &  & \int f_{3}(x)dx & \\ a_{2} &  & b_{2} &  & c_{2} & \\ a_{3} &  & b_{3} &  & c_{3} & \end{vmatrix}\, +\, C$ <br/>
Reason: Integration of sum of several function is equal to sum of integration of individual functions.
Question 33 :
If a continuous function $f$ satisfies $\displaystyle \int_{0}^{x^{2}}f\left ( t \right )\: dt= x^{2}\left ( 1+x \right )$ then $f\left ( 4 \right )$ is equal to
Question 34 :
Integrate the following functions with respect to t: $\displaystyle \int \left ( 3t^{2}-2t \right )dt$<br/>
Question 36 :
 Find Integrals of given function: $\int_{}^{} {\tan \theta } {\tan ^2}\theta {\sec ^2}\theta d\theta $<br/>
Question 38 :
$\displaystyle \int \left \{\dfrac {(\log x - 1)}{1 + (\log x)^{2}}\right \}^{2}dx$ is equal to:
Question 40 :
What is $\displaystyle \int \dfrac{x^4 - 1}{x^2 \sqrt{x^4 + x^2 + 1}} dx$ equal to?
Question 41 :
Let $I_n=\int \tan^n x\,dx, (n > 1)$. If $I_4 +I_6=a \tan^5x+bx^5+C$, where $C$ is a constant of integration, then the ordered pair $(a, b)$ is equal to
Question 42 :
The value of $\displaystyle\int { \dfrac { dx }{ \sqrt { 2x-{ x }^{ 2 } } } } $ is
Question 43 :
$\displaystyle \int \cos \left \{ 2\tan ^{-1}\sqrt{\frac{1-x}{1+x}} \right \}dx$ is equal to
Question 44 :
Integrate the following function with respect to x$\displaystyle \int \left ( 5x^{2}+3x-2 \right )dx$<br/><br/>
Question 45 :
$\displaystyle \int (1 + 2x + 3x^{2} + 4x^{3} + .....) dx (\left | x \right | < 1)$
Question 49 :
<p>The value of $\displaystyle\int {\dfrac{{\ln n\left( {1 - \left(<br/>{\dfrac{1}{x}} \right)} \right)dx}}{{x\left( {x - 1} \right)}}} $ is </p>
Question 52 :
If $\int \sin x d (\sec  x) = f(x) - g(x) + c$, then
Question 56 :
$\displaystyle\int \dfrac { x - 2 } { x ^ { 2 } - 4 x + 3 } d x =$