Question 1 :
Evaluate  $\int _{ 0 }^{ 1 }{ \sqrt { \cfrac { x }{ 1-{ x }^{ 3 } }  }  } dx=$
Question 10 :
$\displaystyle \int {\frac{{xdx}}{{\sqrt {1 + {x^2} + \sqrt {{{(1 + {x^2})}^3}} } }}} $ is equal to :
Question 14 :
The value of $\displaystyle \int \dfrac {(x - 2)dx}{\left \{(x - 2)^{2} (x + 3)^{7}\right \}^{1/3}}$ is
Question 15 :
$\displaystyle \int { \frac { dx }{ { x }^{ 1/5 }{ \left( 1+{ x }^{ 4/5 } \right)  }^{ 1/2 } }  } $ equals
Question 16 :
$\int_{}^{} {\dfrac{{{x^2}}}{{\sqrt {1 - x} }}dx = \int_{}^{} {\dfrac{{{{\left( {1 - u} \right)}^2}}}{{\sqrt u }}\left( { - du} \right)} } $
Question 19 :
$\int \dfrac {x^{2} - 1}{x^{4} + 3x^{2} + 1} dx (x > 0)$ is
Question 23 :
$\displaystyle \int { { \left(\displaystyle  \frac { 1 }{ a } -\displaystyle \frac { 1 }{ x }  \right)  }^{ n } } \displaystyle \frac { 1 }{ { x }^{ 2 } } dx$<br/>
Question 25 :
If $\int {\sqrt {\dfrac{{1 - x}}{{1 + x}}} dx = \sqrt {1 - {x^2}} }  + f\left( x \right) + c,\,x \in [0,\,1)$ where $f\left( 0 \right) =  - \dfrac{\pi }{2}$ then $f\left( {\dfrac{1}{2}} \right)$ is ______
Question 26 :
The solution of integral: $\displaystyle\int { { \left( \sqrt { x } +\frac { 1 }{ \sqrt { x }  }  \right)  }^{ 2 }dx } $ is equal to
Question 35 :
Solve $\displaystyle\int {\dfrac{{2 + x + {x^2}}}{{{x^2}\left( {2 + x} \right)}} + \dfrac{{2x - 1}}{{{{\left( {x + 1} \right)}^2}}}dx} $
Question 37 :
$\displaystyle\int { \dfrac { dx }{ x\sqrt { { x }^{ 6 }-16 } } } $ is equal to
Question 43 :
If $c$ is an arbitrary constant then  $\displaystyle{ {\int\frac { \cos(x+a) }{ \sin(x+b) } dx }} = $
Question 46 :
The integral $\displaystyle \int { \cfrac { x+2 }{ \left( { x }^{ 2 }+3x+3 \right) \sqrt { x+1 }  }  }dx $ is equl to
Question 47 :
$ \displaystyle \int \dfrac {dx}{x - \sqrt{x}} $ is equal to :
Question 49 :
$\displaystyle \int_{-1}^{1} \dfrac{x^3 + |x| + 1}{x^2 + 2|x| + 1} dx$ is equal to
Question 50 :
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 52 :
$\int \cfrac { d x } { \sqrt { 2 a x - x ^ { 2 } } } = a ^ { n } \sin ^ { - 1 } \left[ \cfrac { x } { a } - 1 \right]$ <br/>The value of $n$ is<br/>
Question 53 :
$\int {\sqrt {x + a\sqrt {ax - {a^2}} } \,dx,0 < a < 2 = \frac{2}{{{a^{\frac{3}{2}}}}}{{\left\{ {ax + a\sqrt {ax - {a^2}} } \right\}}^{\frac{3}{2}}} - \frac{{\sqrt a }}{2}\left[ {A + B} \right]} + c$. Then
Question 55 :
$\displaystyle\int { \dfrac { dx }{ x+\sqrt { x } } } $ equals
Question 57 :
$\displaystyle\int { \sqrt { x } { e }^{ \sqrt { x } }dx } $ is equal to
Question 58 :
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 59 :
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 61 :
$\displaystyle \int { \dfrac { \left( x+2 \right) dx }{ \sqrt { \left( x-2 \right) \left( x-3 \right)  }  }  }$ is equal to:
Question 62 :
$\displaystyle \int \dfrac {(x + 3)e^{x}}{(x + 4)^{2}}dx$ is equal to
Question 63 :
Let $F(x)$ be the primitive of $\displaystyle\frac{3x+2}{\sqrt{x-9}}$ with respect to $x$. If $F(10)=60$, then the value of $F(13)$ is equal to
Question 65 :
If $M= \displaystyle \int _{ 0 }^{ \pi /2 }{ \cfrac { \cos { x }  }{ x+2 }  } dx,N=\int _{ 0 }^{ \pi /4 }{ \cfrac { \sin { x } \cos { x }  }{ { \left( x+1 \right)  }^{ 2 } }  } dx\quad $, then the value of $M-N$ is ?
Question 66 :
If $f\left(\displaystyle\frac{3x-4}{3x+4}\right)=x+2, x\neq -\displaystyle\frac{4}{3}$, and $\displaystyle\int f(x)dx=A\log |1-x|+Bx+C$, then the ordered pair $(A, B)$ is equal to (where C is a constant of integration)
Question 68 :
The integral $\displaystyle\int {\dfrac{{2{x^{12}} + 5{x^9}}}{{{{\left( {{x^5} + {x^3} + 1} \right)}^3}}}dx} $ is equal to
Question 72 :
Evaluate: $\displaystyle \int { \dfrac { x\sqrt { x } .dx }{ \sqrt { 1-{ x }^{ 5 } }  } } $
Question 75 :
. Let $\displaystyle \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{(1+\mathrm{x}^{\mathrm{n}})^{1/\mathrm{n}}}$ for $\mathrm{n}\geq 2$ and $\displaystyle \mathrm{g}(\mathrm{x})=\frac{(\mathrm{f}\mathrm{o}\mathrm{f}\mathrm{o}\ldots \mathrm{o}\mathrm{f})}{\mathrm{f}\mathrm{o}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{s}}(\mathrm{x})$ . Then $\displaystyle \int \mathrm{x}^{\mathrm{n}-2}\mathrm{g}$ (x)dx equals <br><br>
Question 76 :
Integrate <br/>$\displaystyle\int {\dfrac{{dx}}{{\left( {x + 1} \right)\sqrt {2{x^2} + 3x + 1} }}} $
Question 78 : <div><span>If $\displaystyle I = \int \frac {\sin (x + \alpha) + \cos x}{\sin (x - \alpha)} dx$, then I equals</span><br/></div>
Question 79 :
If $\displaystyle{\int \frac{\displaystyle dx}{\displaystyle \sqrt{x}+\displaystyle \sqrt[3]{x}}}=a\sqrt{x}+b(\sqrt[3]{x})+c(\sqrt[6]{x})+d\: \ln(\sqrt[6]{x}+1)+e$, $e$ being arbitrary constant then. Find the value of $20a + b + c + d.$<br/>
Question 80 :
$\displaystyle \int \sqrt {1+x \sqrt {1+(x+1) \sqrt {1+(x+2) (x+4)}}}$ $dx$ is equal to
Question 82 :
Solution of the differential equation<br>$\left \{\dfrac {1}{x} - \dfrac {y^{2}}{(x - y)^{2}}\right \} dx + \left \{\dfrac {x^{2}}{(x - y)^{2}} - \dfrac {1}{y}\right \} dy = 0$ is<br>(where $c$ is arbitrary constant).
Question 84 :
$\displaystyle\int { \dfrac { 1 }{ { x }^{ 2 }{ \left( { x }^{ 4 }+1 \right) }^{ { 3 }/{ 4 } } } dx } $ is equal to
Question 86 :
$\displaystyle\int { \cfrac { \left( 2{ x }^{ 12 }+5{ x }^{ 9 } \right)  }{ { \left( 1+{ x }^{ 3 }+{ x }^{ 5 } \right)  }^{ 3 } }  } dx$ equals
Question 89 :
If $f\left( \cfrac { 3x-4 }{ 3x+4 } \right) =x+2$, then $\int { f(x) } dx$ is
Question 90 :
Evaluate: $\displaystyle \int _{ 0 }^{ \tfrac { \pi  }{ 4 }  }{ \cfrac { \sin { x } +\cos { x }  }{ 7+9\sin { 2x }  }  } dx$
Question 93 :
$\displaystyle \int \dfrac {1}{x^{2}(x^{4} + 1)^{3/4}} dx$ is equal to ____
Question 94 :
$\displaystyle \int \frac{x\quad dx}{\sqrt{1 + x^{2} + \sqrt{(1 + x^{2})^{3}}}}$ is equal to
Question 96 :
If $I =\displaystyle \int {\dfrac{{dx}}{{{{\left( {2ax + {x^2}} \right)}^{\frac{3}{2}}}}}} $, then $I$ is equal to
Question 97 :
If $\int { f\left( x \right) dx=\Psi \left( x \right) }$, then $\int { { x }^{ 5 }f\left( { x }^{ 3 } \right) } dx$ is equal to:
Question 103 :
$\displaystyle \int { \frac { 1+x }{ 1+\sqrt [ 3 ]{ x }  } dx } $ is equal to
Question 106 :
$\displaystyle\int { \dfrac { x+2 }{ \left( { x }^{ 2 }+3x+3 \right) \sqrt { x+1 } } dx } $ is equal to
Question 108 :
If $\displaystyle I = \int tan^{-1} \sqrt {\left ( \sqrt x - 1 \right )} dx = (u^2 + 1)^2 tan^{-1} u - \frac {A}{1863} u^3 - u + C$ where $\displaystyle u = \sqrt {\sqrt x - 1}$ then A is equal to.
Question 110 :
Integrate the given equation $\int { \dfrac { \sqrt { { x }^{ 2 }+1 } (\log { \left( { x }^{ 2 }+1 \right) -2\log { x })  }  }{ { x }^{ 4 } }  } dx$
Question 112 :
The value of the expression $\dfrac{\int_{0}^{a} x^{4} \sqrt{a^{2}-x^{2}} d x}{\int_{0}^{a} x^{2} \sqrt{a^{2}-x^{2}} d x}$ is equal to
