Question 3 :
What is $\displaystyle \int \dfrac{dx}{x(1 + ln x)^n}$ equal to $(n \neq 1)$ ?
Question 4 :
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 17 :
The derivative of $x^{-4} + x^{-5}$ is $-(4x^{-5} + 5x^{-6})$. So, $\displaystyle\int \dfrac{5x^4 + 4x^5}{(x^5 + x + 1)^2}dx$ is equal to
Question 21 :
Integrate the following functions with respect to t: $\displaystyle \int \left ( 3t^{2}-2t \right )dt$<br/>
Question 22 :
$\displaystyle \int \frac{\sin x+\cos x}{\sqrt{\left ( 1+\sin 2x \right )}}$dx is
Question 23 :
The value of $\displaystyle\int { \dfrac { dx }{ \left( 1+{ x }^{ 2 } \right) \sqrt { 1-{ x }^{ 2 } } } } $ is
Question 26 :
If $\int \dfrac {1}{1 + \sin x}dx = \tan \left (\dfrac {x}{2} + a\right ) + b$, then
Question 28 :
What is $\int { (x^2 + 1)^{\frac{5}{2}}xdx}$ equal to ?<br>Where c is a constant of integration.
Question 29 :
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 31 :
Integrate the following function with respect to x$\displaystyle \int \left ( 5x^{2}+3x-2 \right )dx$<br/><br/>
Question 32 :
$\int \dfrac {x^{2} - 1}{x^{4} + 3x^{2} + 1} dx (x > 0)$ is
Question 33 :
If $\dfrac {dy}{dt} = ky$ and $k\neq 0$, which of the following could be the equation of $y$?
Question 35 :
If $g(1)=g(2)$ then the value of  $\int _{ 1 }^{ 2 }{ { \left[ f\{ g(x)\}  \right]  }^{ -1 } } f'\{ g(x)\} g'(x)dx\quad is$
Question 36 :
Evaluate: $\displaystyle\int \dfrac{\sin^3x}{( \cos^4x+ 3 \cos^2x+ 1)\tan^{-1} ( \sec x+ \cos x)}dx$
Question 37 :
If $\int \sin x d (\sec  x) = f(x) - g(x) + c$, then
Question 38 :
<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 41 :
$\displaystyle \int \left \{\dfrac {(\log x - 1)}{1 + (\log x)^{2}}\right \}^{2}dx$ is equal to:
Question 42 :
$\int { \left( \cfrac { 4{ e }^{ x }-25 }{ 2{ e }^{ x }-5 } \right) } dx=Ax+B\log { \left| 2{ e }^{ x }-5 \right| } +c$, then
Question 43 :
$\displaystyle \int { \dfrac { \left( x+2 \right) dx }{ \sqrt { \left( x-2 \right) \left( x-3 \right)  }  }  }$ is equal to:
Question 44 :
If $g\left( x \right) =\int { { x }^{ x }\log _{ e }{ (ex)dx }  } $ then  $g\left( \pi \right) $ equals
Question 46 :
If $\int \sqrt 2\sqrt{1+\sin x}dx = -4 \cos(ax+b)+c$, then the value of a,b are:
Question 47 :
$\int { \dfrac { { x }^{ e-1 }+{ e }^{ x-1 } }{ { x }^{ e }+{ e }^{ x } } dx } $ is equal to
Question 48 :
$\displaystyle\int { \cfrac { 1 }{ 7 } \sin { \left( \cfrac { x }{ 7 } +10 \right)  } dx } $ is equal to