Question 1 :
$\displaystyle \int_{}^{} {{{\tan }^{ - 1}}\sqrt {\dfrac{{1 - \cos 2x}}{{1 + \cos 2x}}} dx} $, where $0 < x < \dfrac{\pi }{2}$ is equal to
Question 3 :
<div><span>State the following statement is True or False</span><br/></div>Integration of constant is zero.<br/>
Question 7 :
The value of $\displaystyle\int { \cfrac { 2 }{ { \left( { e }^{ x }+{ e }^{ -x } \right) }^{ 2 } } } dx$ is
Question 11 :
If a curve passes through the point $\left( 2,\cfrac { 7 }{ 2 } \right) $ and has slope $\left( 1-\cfrac { 1 }{ { x }^{ 2 } } \right) $ at any point $(x,y)$ on it, then the ordinate of the point on the curve whose abscissa is $-2$ is:
Question 12 :
$\int {\dfrac{{\cot \sqrt x }}{{2\sqrt x }}dx} $ is equal to $ = \_\_\_\_\_ + C.$
Question 13 :
$\int \dfrac {dx}{\sqrt {x^{10} - x^{2}}}; x > 1=$ ______ $+ C$.
Question 16 :
<div>Integrate the following function:</div>$\displaystyle \int { \dfrac { { d }^{ 2 } }{ { dx }^{ 2 } } } \left( \sin ^{ -1 }{ x } \right) dx$
Question 18 :
If $\phi (x) = f(x) + xf^1 (x)$ then $\int {\phi (x)dx} $ is equal to
Question 20 :
If $\displaystyle \int { \frac { 1 }{ x+{ x }^{ 5 } } dx } =f\left( x \right)+c$, then $\displaystyle \int { \frac { { x }^{ 4 } }{ x+{ x }^{ 5 } } dx } $ is equal to
Question 21 :
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 22 :
<span>$\displaystyle \int { \frac { dx }{ \left( 1+\sqrt { x } \right) \sqrt { x-{ x }^{ 2 } } } } $ is equal to<br></span>
Question 23 :
$\displaystyle \int \frac{\sin x+\cos x}{\sqrt{\left ( 1+\sin 2x \right )}}$dx is
Question 26 :
The value of $\int \dfrac { d x } { x \sqrt { 1 - x ^ { 3 } } }$ is equal to
Question 27 :
What is $\int \dfrac {xe^{x}dx}{(x + 1)^{2}}$ equal to?<br>where $c$ is the constant of integration.
Question 29 :
$\displaystyle \int { \dfrac { 1 }{ \sqrt { 4-3x } } } dx=\_ \_ \_ \_ \_ \_ +c$
Question 30 :
$\int {{e^x}(\log \sin x + \cot x)\,dx = } \_\_\_\_\_\_ + C.$