Question 7 :
The value of $\displaystyle\int \dfrac{\cos\ 2\ x}{\cos\ x}\ dx$ is equal to

Question 8 :
What is $\displaystyle \int \dfrac{dx}{x(1 + ln x)^n}$ equal to $(n \neq 1)$ ?

Question 14 :
$\int { \sqrt { secx-1 } } dx$ is equal to

Question 16 :
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 18 :
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 20 :
$\displaystyle \int \dfrac{(\sin x )^{99}}{(\cos x)^{101}} dx$ =&#160; _______ $+ c$

Question 21 :
The value of $\displaystyle\int { \dfrac { dx }{ \left( 1+{ x }^{ 2 } \right) \sqrt { 1-{ x }^{ 2 } } } } $ is

Question 22 :
$\displaystyle \int \dfrac{1}{\sqrt{x}} \tan^4 \, \sqrt{x} \, \sec^2 \, \sqrt{x} \, dx = $

Question 25 :
If $\displaystyle \int f(x)dx= g(x)$ and $\displaystyle \int f(x)dx= h(x)$ then <br>

Question 27 :
$\int {{{(\sin x)}^{99}}{{(\cos x)}^{ - 101}}dx = \_\_\_\_\_\_\_ + C.} $

Question 30 :
The value of the definite integral<br/>$\overset { { a }_{ 1 } }{ \underset { { a }_{ 2 } }{ \int { \frac { d\theta&#160; }{ 1+tan\theta&#160; }&#160; }&#160; }&#160; } =\frac { 501\pi&#160; }{ K } $ where $\ a _{ 2 }=\quad \frac { 1003\pi&#160; }{ 2008 } $ and ${ \ a&#160; }_{ 1 }=\frac { \pi&#160; }{ 2008 } $ The value of K equalls

Question 31 :
The integral $\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$ is equal to?(Here C is a constant of integration)

Question 32 :
The value of $\displaystyle \int \dfrac{1}{\sin \left( x - \dfrac{\pi}{3}\right) \cos x} dx$is

Question 34 :
$\displaystyle \int (1 + x - x^{-1})e^{x + x^{-1}}dx$ is equal to

Question 35 :
Integrate the following functions with respect to t:&#160;$\displaystyle \int \left ( 3t^{2}-2t \right )dt$<br/>

Question 36 :
The value of $\displaystyle\int { \dfrac { dx }{ \sqrt { 2x-{ x }^{ 2 } } } } $ is

Question 37 :
If $\dfrac {dy}{dt} = ky$ and $k\neq 0$, which of the following could be the equation of $y$?

Question 40 :
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 42 :
If $\int_{1}^{2} e^{x^{2}} d x=a,$ then $\int_{e}^{e^{4}} \sqrt{\ln x} d x$ is equal to

Question 44 :
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/>

Question 46 :
Let $f\left( x \right) $ be a polynomial of degree three satisfying $f\left( 0 \right) =-1$ and $f(1)=0$. Also, $0$ is a stationary point of $f(x)$. If $f(x)$ does not have an extremum at $x=0$, then $\displaystyle\int { \frac { f\left( x \right) }{ { x }^{ 3 }-1 } dx } $ is equal to

Question 47 :
$\int \frac { \cos x + 2 \sin x } { 7 \sin x - 5 \cos x } d x = a x + b \ln | 7 \sin x - 5 \cos x | + c$ then $a+b$ is