Question Text
Question 1 :
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 10 :
$$\int { \sqrt { secx-1 } } dx$$ is equal to
Question 12 :
The value of $$\displaystyle\int \dfrac{\cos\ 2\ x}{\cos\ x}\ dx$$ is equal to
Question 16 :
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 19 :
$$\displaystyle \int \dfrac{\sin x \cos x }{\sqrt{1 - \sin^4 x}}dx$$ is equal to
Question 20 :
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 22 :
What is $$\displaystyle \int \dfrac{dx}{2x^2 - 2x + 1}$$ equal to ?
Question 23 :
$$\int \frac { \cos x + 2 \sin x } { 7 \sin x - 5 \cos x } d x = a x + b \ln | 7 \sin x - 5 \cos x | + c$$ then $$a+b$$ is
Question 24 :
$$\int {{{(\sin x)}^{99}}{{(\cos x)}^{ - 101}}dx = \_\_\_\_\_\_\_ + C.} $$
Question 25 :
$$\displaystyle\int { \dfrac { dx }{ x+\sqrt { x } } } $$ is equal to
Question 29 :
$$\int \dfrac{cos 2x - cos 2 \theta}{cos x - cos \theta} dx$$ is equal to
Question 30 :
$$\displaystyle \int \dfrac { \cot ^ { 2 } x } { \left( cosec ^ { 2 } x + cosec x \right) } d x =$$