Question 3 :
The value of $\displaystyle\int \dfrac{\cos\ 2\ x}{\cos\ x}\ dx$ is equal to
Question 7 :
$\int { \sqrt { secx-1 } } dx$ is equal to
Question 8 :
What is $\displaystyle \int \dfrac{dx}{x(1 + ln x)^n}$ equal to $(n \neq 1)$ ?
Question 19 :
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 20 :
The value of $\int \dfrac { d x } { x \sqrt { 1 - x ^ { 3 } } }$ is equal to
Question 21 :
What is $\int { (x^2 + 1)^{\frac{5}{2}}xdx}$ equal to ?<br>Where c is a constant of integration.
Question 22 :
$\displaystyle\int { \dfrac { dx }{ x+\sqrt { x } } } $ equals
Question 24 :
The integral $\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$ is equal to?(Here C is a constant of integration)
Question 25 :
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 26 :
If $\int \dfrac {1}{1 + \sin x}dx = \tan \left (\dfrac {x}{2} + a\right ) + b$, then
Question 28 :
$\displaystyle \int \dfrac{1}{\sqrt{x}} \tan^4 \, \sqrt{x} \, \sec^2 \, \sqrt{x} \, dx = $
Question 29 :
$\displaystyle\int { \frac { dx }{ \left( 1+\sqrt { x } \right) \sqrt { x-{ x }^{ 2 } } } } $ is equal to<br>
Question 31 :
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 32 :
$\int \dfrac {x^{2} - 1}{x^{4} + 3x^{2} + 1} dx (x > 0)$ is
Question 33 :
The integral $\displaystyle \int { \cfrac { x+2 }{ \left( { x }^{ 2 }+3x+3 \right) \sqrt { x+1 }  }  }dx $ is equl to
Question 35 :
If $\displaystyle \int f(x)dx =2\{f(x)\}^{3}+c {\it}$,  and $f(x) \neq 0$   then $f(x)$ is<br/>
Question 37 :
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 39 :
$\displaystyle\int { \dfrac { dx }{ x+\sqrt { x } } } $ is equal to
Question 40 :
$\displaystyle \int \dfrac {3^{x}}{\sqrt {1 - 9^{x}}} dx$ is equal to
Question 41 :
$\int { \left( \cfrac { 4{ e }^{ x }-25 }{ 2{ e }^{ x }-5 } \right) } dx=Ax+B\log { \left| 2{ e }^{ x }-5 \right| } +c$, then
Question 42 :
$\displaystyle \overset{e^2}{\underset{1}{\int}} [log_e \,x]dx, x > 0$ and $[\cdot]$ is greatest integer function, is equal to
Question 44 :
$\displaystyle \int (1 + 2x + 3x^{2} + 4x^{3} + .....) dx (\left | x \right | < 1)$
Question 46 :
$\displaystyle \int \dfrac {\sin x + \cos x}{e^{-x} + \sin x} dx$ is equal to
Question 47 :
$\int {{{(\sin x)}^{99}}{{(\cos x)}^{ - 101}}dx = \_\_\_\_\_\_\_ + C.} $
Question 48 :
 Find Integrals of given function: $\int_{}^{} {\tan \theta } {\tan ^2}\theta {\sec ^2}\theta d\theta $<br/>
Question 49 :
If the anti-derivative of $\displaystyle \int \frac{\sin^4 x}{x} dx$ is $f(x)$, then $\displaystyle \int \frac{\sin^4 \{ (p + q)x \}}{x} dx$ in terms of $f(x)$ is