Question 2 :
What is $\displaystyle \int \dfrac{dx}{x(1 + ln x)^n}$ equal to $(n \neq 1)$ ?
Question 5 :
$\int { \sqrt { secx-1 } } dx$ is equal to
Question 11 :
The value of $\displaystyle\int \dfrac{\cos\ 2\ x}{\cos\ x}\ dx$ is equal to
Question 12 :
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 21 :
$\displaystyle \int \left \{\dfrac {(\log x - 1)}{1 + (\log x)^{2}}\right \}^{2}dx$ is equal to:
Question 23 :
The value of the integral $\displaystyle \int \frac{e^{7\log x} - e^{6\log x}}{e^{5\log x} - e^{4 \log x}} dx$ is equal to<br/>
Question 24 :
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 27 :
If $\displaystyle\int\dfrac{\sqrt{1-x^2}}{x^4}dx=A(x)(\sqrt{1-x^2})+C$, fora suitable chosen integer m and a function<br>A(x), where C is a constant of integration then $(A(x)) ^m $ equals :
Question 28 : <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 29 :
$\displaystyle \int { \dfrac { \left( x+2 \right) dx }{ \sqrt { \left( x-2 \right) \left( x-3 \right)  }  }  }$ is equal to:
Question 31 :
If $\int \sqrt 2\sqrt{1+\sin x}dx = -4 \cos(ax+b)+c$, then the value of a,b are:
Question 33 :
The integral $\displaystyle\int \dfrac{\sin^2x \cos^2x}{(\sin^5x+ \cos^3x \sin^2 x+ \sin^3x \cos^2x + \cos^5x)^2}dx$
Question 35 :
$\displaystyle\int { \dfrac { dx }{ x+\sqrt { x } } } $ equals
Question 36 :
The value of $\displaystyle\int { \cfrac { \sin { x } +\cos { x }  }{ 3+\sin { 2x }  }  } dx$ is
Question 38 :
$f(x), g(x)$ 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 39 :
$\displaystyle\int { \cfrac { 1 }{ 7 } \sin { \left( \cfrac { x }{ 7 } +10 \right)  } dx } $ is equal to
Question 42 :
Integrate the following functions with respect to t: $\displaystyle \int \left ( 3t^{2}-2t \right )dt$<br/>
Question 43 :
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 45 :
$\displaystyle\int \dfrac { x - 2 } { x ^ { 2 } - 4 x + 3 } d x =$ 
Question 46 :
The number of integral solutions $( x , y )$of the equations $x \sqrt { y } + y \sqrt { x } = 20$ and $x \sqrt { x } + y \sqrt { y } = 65$ is :
Question 47 :
$\displaystyle \overset{e^2}{\underset{1}{\int}} [log_e \,x]dx, x > 0$ and $[\cdot]$ is greatest integer function, is equal to
Question 48 :
$\int { \left( \cfrac { 4{ e }^{ x }-25 }{ 2{ e }^{ x }-5 } \right) } dx=Ax+B\log { \left| 2{ e }^{ x }-5 \right| } +c$, then
Question 50 :
$\int \frac { \cos x + 2 \sin x } { 7 \sin x - 5 \cos x } d x = a x + b \ln | 7 \sin x - 5 \cos x | + c$ then $a+b$ is
Question 51 :
If $\displaystyle \int _0^{\pi/2} \sin x \cos x dx $ is equal to:
Question 52 :
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 54 :
The value of $\int {{x \over {\sqrt {{x^4} + {x^2} + 1} }}dx} $ equals
Question 55 :
If $\int { \cfrac { 1-{ \left( \cot { x } \right) }^{ 2010 } }{ \tan { x } +{ \left( \cot { x } \right) }^{ 2011 } } dx } =\cfrac { 1 }{ k } \log _{ e }{ \left| { \left( \sin { x } \right) }^{ k }+{ \left( \cos { x } \right) }^{ k } \right| } +C$, then $k$ is equal to
Question 62 :
$\displaystyle \int \dfrac {3^{x}}{\sqrt {1 - 9^{x}}} dx$ is equal to
Question 64 :
The value of $\int_{1}^{e} \dfrac{1+x^{2} \ln x}{x+x^{2} \ln x} d x$ is
Question 68 :
The anti derivative of $\displaystyle \left (\sqrt x+\frac {1}{\sqrt x}\right )$ equals<br>
Question 69 :
The value of $\displaystyle\int { \dfrac { dx }{ \sqrt { 2x-{ x }^{ 2 } } } } $ is
