Question Text
Question 3 :
What is $\displaystyle \int \dfrac{dx}{x(1 + ln x)^n}$ equal to $(n \neq 1)$ ?
Question 6 :
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 11 :
$\displaystyle \int \left \{\dfrac {(\log x - 1)}{1 + (\log x)^{2}}\right \}^{2}dx$ is equal to:
Question 12 :
$\int _{ 0 }^{ \pi /4 }{ \cfrac { \sec ^{ 2 }{ x } }{ \left( 1+\tan { x } \right) \left( 2+\tan { x } \right) } dx } $ equals:
Question 13 :
$\displaystyle \int \dfrac {\sin x + \cos x}{e^{-x} + \sin x} dx$ is equal to
Question 15 :
$\int {{{(\sin x)}^{99}}{{(\cos x)}^{ - 101}}dx = \_\_\_\_\_\_\_ + C.} $
Question 20 :
The value of $\int_{1}^{e} \dfrac{1+x^{2} \ln x}{x+x^{2} \ln x} d x$ is
Question 21 :
If $\int \frac { x ^ { 2 } \tan ^ { - 1 } x } { 1 + x ^ { 2 } } d x = \tan ^ { - 1 } x - \frac { 1 } { 2 } \log \left( 1 + x ^ { 2 } \right) + f ( x ) + c$ then $f ( x ) =$
Question 23 :
The value of the integral $\displaystyle \int \frac{e^{7\log x} - e^{6\log x}}{e^{5\log x} - e^{4 \log x}} dx$ is equal to<br/>
Question 24 :
$\displaystyle \int (1 + 2x + 3x^{2} + 4x^{3} + .....) dx (\left | x \right | < 1)$
Question 26 :
The value of $\displaystyle\int { \dfrac { dx }{ \sqrt { 2x-{ x }^{ 2 } } } } $ is
Question 28 :
Evaluate $\displaystyle\int { \left( \dfrac { 1 }{ 7 } -\dfrac { 1 }{ { y}^{ 5/4 } }  \right)  }dy$
Question 29 :
What is $\int { (x^2 + 1)^{\frac{5}{2}}xdx}$ equal to ?<br>Where c is a constant of integration.