Question 9 :
The value of $\displaystyle\int \dfrac{\cos\ 2\ x}{\cos\ x}\ dx$ is equal to

Question 15 :
What is $\displaystyle \int \dfrac{dx}{x(1 + ln x)^n}$ equal to $(n \neq 1)$ ?

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 :
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 21 :
$\displaystyle \int \dfrac{(\sin x )^{99}}{(\cos x)^{101}} dx$ =&#160; _______ $+ c$

Question 22 :
Integrate the following function with respect to x$\displaystyle \int \left ( 5x^{2}+3x-2 \right )dx$<br/><br/>

Question 23 :
$\displaystyle \overset{e^2}{\underset{1}{\int}} [log_e \,x]dx, x &gt; 0$ and $[\cdot]$ is greatest integer function, is equal to

Question 25 :
What is $\displaystyle \int \dfrac{x^4 - 1}{x^2 \sqrt{x^4 + x^2 + 1}} dx$ equal to?

Question 26 :
The integral $\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$ is equal to?(Here C is a constant of integration)

Question 27 :
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 29 :
If the anti-derivative of $\displaystyle \int \frac{\sin^4 x}{x} dx$ is $f(x)$, then $\displaystyle \int \frac{\sin^4 \{ (p + q)x \}}{x} dx$ in terms of $f(x)$ is

Question 30 :
$\displaystyle \int (1 + x - x^{-1})e^{x + x^{-1}}dx$ is equal to

Question 36 :
The value of&#160;$\displaystyle \int {\dfrac{{d({x^2} + 1)}}{{\sqrt {{x^2} + 2} }}} ,$ is&#160;

Question 38 :
$\int { \cfrac { 1 }{ 8\sin ^{ 2 }{ x } +1 } } dx$ is equal to

Question 39 :
Let f be a function defined for every x, such that&#160;f'' = -f ,f(0)=0, f' (0) = 1, then f(x) is equal to

Question 40 :
Solve: $\displaystyle \int \dfrac{\sin 2x}{\sin \left(x - \dfrac{\pi}{4}\right) .\sin \left(x + \dfrac{\pi}{4}\right)} dx$

Question 42 :
$\int \dfrac{cos 2x - cos 2 \theta}{cos x - cos \theta} dx$ is equal to

Question 45 :
$\displaystyle&#160;\int { \frac { \sqrt { x } &#160;}{ \sqrt { { x }^{ 3 }+4 } &#160;} dx } $ is equal to

Question 47 :
The integral $\displaystyle \int{\frac{\sec^2 x}{\left(\sec x + \tan x \right)^{9/2}}}$ dx equals (for some arbitrary constant $k$)<br>