Question 1 :
$\displaystyle \int {\frac{{xdx}}{{\sqrt {1 + {x^2} + \sqrt {{{(1 + {x^2})}^3}} } }}} $ is equal to :
Question 11 :
Evaluate  $\int _{ 0 }^{ 1 }{ \sqrt { \cfrac { x }{ 1-{ x }^{ 3 } }  }  } dx=$
Question 13 :
If $\displaystyle\int\dfrac{\sqrt{1-x^2}}{x^4}dx=A(x)(\sqrt{1-x^2})+C$, for a suitable chosen integer m and a function<br>A(x), where C is a constant of integration then $(A(x)) ^m $ equals :
Question 18 :
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 19 :
$\displaystyle \int { \frac { \sec { x }  }{ \sqrt { \sin { \left(2 x+\alpha  \right)  } +\sin { \alpha  }  }  } dx } =$
Question 22 :
$\displaystyle \int { \cfrac { x }{ 1+{ x }^{ 4 } }  } dx$ is equal to
Question 25 :
If $f(x)=\int \dfrac{5x^8+7x^6}{(x^2+1+2x^7)^2}dx,(x\ge0)$ and $f(0)=0$, the the value of $f(1)$ is:
Question 27 :
$\int {\sqrt {x + a\sqrt {ax - {a^2}} } \,dx,0 < a < 2 = \frac{2}{{{a^{\frac{3}{2}}}}}{{\left\{ {ax + a\sqrt {ax - {a^2}} } \right\}}^{\frac{3}{2}}} - \frac{{\sqrt a }}{2}\left[ {A + B} \right]} + c$. Then
Question 28 :
If $c$ is an arbitrary constant then  $\displaystyle{ {\int\frac { \cos(x+a) }{ \sin(x+b) } dx }} = $
Question 30 :
$\displaystyle\int { \dfrac { dx }{ x+\sqrt { x } } } $ is equal to
Question 32 :
<span>Integrate the following functions with respect to x: </span>$\displaystyle \int \left ( 6x+2 \right )^{3} dx$<br/>
Question 34 :
The value of $\displaystyle\int { \dfrac { dx }{ \left( 1+{ x }^{ 2 } \right) \sqrt { 1-{ x }^{ 2 } } } } $ is
Question 37 :
$\displaystyle \int { \frac { dx }{ { x }^{ 1/5 }{ \left( 1+{ x }^{ 4/5 } \right)  }^{ 1/2 } }  } $ equals
Question 38 :
$ \displaystyle \int \dfrac {dx}{x - \sqrt{x}} $ is equal to :
Question 42 :
If $\displaystyle \int { { x }^{ \frac { 13 }{ 2 } }.{ \left( 1+{ x }^{ \frac { 5 }{ 2 } } \right) }^{ \frac { 1 }{ 2 } }dx } =A{ \left( 1+{ x }^{ \frac { 5 }{ 2 } } \right) }^{ \frac { 7 }{ 2 } }+B{ \left( 1+{ x }^{ \frac { 5 }{ 2 } } \right) }^{ \frac { 5 }{ 2 } }+C{ \left( 1+{ x }^{ \frac { 5 }{ 2 } } \right) }^{ \frac { 3 }{ 2 } }$, then
Question 45 :
$\displaystyle \int \dfrac {1 + x^{4}}{(1 - x^{4})^{3/2}}dx$ is equal to
Question 46 :
The integral $\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$ is equal to?(Here C is a constant of integration)
Question 49 :
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 50 :
$\int { \cfrac { { x }^{ 2 }+1 }{ x({ x }^{ 2 }-1) } dx } $ is equal to
Question 51 :
$\displaystyle \int\dfrac{dx}{(x + 100)\sqrt{x + 99}} = f(x) + c \Longrightarrow f(x) =$
Question 53 :
$\displaystyle\int { \dfrac { dx }{ x\sqrt { { x }^{ 6 }-16 } } } $ is equal to
Question 57 : <div>Evaluate the given integral.<br/></div>$\displaystyle\int { \cfrac { { x }^{ 9 } }{ { \left( 4{ x }^{ 2 }+1 \right)  }^{ 6 } }  } dx $ 
Question 58 :
$\displaystyle \int { \cfrac { dx }{ x\left( { x }^{ 4 }-1 \right)  }  } =$
Question 61 :
$\displaystyle\int { \dfrac { { x }^{ 5 } }{ \sqrt { 1+{ x }^{ 3 } } } dx } $ is equal to
Question 62 :
$\int_{}^{} {\dfrac{{{x^2}}}{{\sqrt {1 - x} }}dx = \int_{}^{} {\dfrac{{{{\left( {1 - u} \right)}^2}}}{{\sqrt u }}\left( { - du} \right)} } $
