Question 1 :
$$\displaystyle \int \dfrac{\sin x \cos x }{\sqrt{1 - \sin^4 x}}dx$$ is equal to
Question 4 :
If$$\displaystyle I = \int \frac {dx}{(e^x + 2)^3}$$, then I equals
Question 6 :
The integral $$\displaystyle\int \dfrac{\sin^2x \cos^2x}{(\sin^5x+ \cos^3x \sin^2 x+ \sin^3x \cos^2x + \cos^5x)^2}dx$$
Question 7 :
$$\displaystyle \int {\frac {1}{x \sqrt{x^2 - 1} } } dx $$ is equal to :
Question 9 :
If $$f'(x) = x + \dfrac {1}{x}$$, then value of $$f(x)$$ is
Question 10 :
The value of $$\int {{x \over {\sqrt {{x^4} + {x^2} + 1} }}dx} $$ equals
Question 11 :
The integral $$\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$$ is equal to?(Here C is a constant of integration)
Question 13 :
$$\int _{ 0 }^{ \pi /4 }{ \cfrac { \sec ^{ 2 }{ x } }{ \left( 1+\tan { x } \right) \left( 2+\tan { x } \right) } dx } $$ equals:
Question 15 :
$$\int \dfrac {2x + 5}{\sqrt {7 - 6x - x^{2}}} dx = A\sqrt {7 - 6x - x^{2}} + B\sin^{-1} \left (\dfrac {x + 3}{4}\right ) + C$$<br>(where $$C$$ is a constant of integration), then the ordered pair $$(A, B)$$ is equal to
Question 16 :
The value of $$\displaystyle\int { \cfrac { \sin { x } +\cos { x }  }{ 3+\sin { 2x }  }  } dx$$ is
Question 17 :
$$\displaystyle \int \dfrac{(\sin x )^{99}}{(\cos x)^{101}} dx$$ =  _______ $$+ c$$
Question 21 :
If $$\int \frac{x\, cos\,  \alpha+1 }{(x^2+2x\, cos\,  \alpha+1)^{3/2}}$$ $$dx= \frac{x}{\sqrt{f(x) + g(x)cos\, \alpha }}+c$$ then (more than one option is correct)<br/>
Question 22 :
If $$\int_{1}^{2} e^{x^{2}} d x=a,$$ then $$\int_{e}^{e^{4}} \sqrt{\ln x} d x$$ 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 :
Evaluate $$\displaystyle\int { \left( \dfrac { 1 }{ 7 } -\dfrac { 1 }{ { y}^{ 5/4 } }  \right)  }dy$$
Question 27 :
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 28 :
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 29 :
$$\displaystyle\int { \dfrac { dx }{ x+\sqrt { x } } } $$ is equal to