Question Text
Question 3 :
If $\displaystyle\int\dfrac{\sqrt{1-x^2}}{x^4}dx=A(x)(\sqrt{1-x^2})+C$, fora suitable chosen integer m and a function<br>A(x), where C is a constant of integration then $(A(x)) ^m $ equals :
Question 4 :
Let $f\left( x \right) $ be a polynomial of degree three satisfying $f\left( 0 \right) =-1$ and $f(1)=0$. Also, $0$ is a stationary point of $f(x)$. If $f(x)$ does not have an extremum at $x=0$, then $\displaystyle\int { \frac { f\left( x \right) }{ { x }^{ 3 }-1 } dx } $ is equal to
Question 7 :
$\int \frac { \cos x + 2 \sin x } { 7 \sin x - 5 \cos x } d x = a x + b \ln | 7 \sin x - 5 \cos x | + c$ then $a+b$ is
Question 8 :
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
Question 9 :
If $\int \dfrac {1}{1 + \sin x}dx = \tan \left (\dfrac {x}{2} + a\right ) + b$, then
Question 12 :
If $\displaystyle \int f(x)dx= g(x)$ and $\displaystyle \int f(x)dx= h(x)$ then <br>
Question 14 :
$\displaystyle \int \dfrac {\sin x + \cos x}{e^{-x} + \sin x} dx$ is equal to
Question 15 :
Integrate the following function with respect to x$\displaystyle \int \left ( 5x^{2}+3x-2 \right )dx$<br/><br/>