If $\int \frac{\sin ^8 x-\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x} d x=A \sin 2 x+B$,then $A$ is equal to

Let a function $h(x)$ be defined as $h(x) = 0$, for all $x \ne 0$. Also $\int_{-\infty}^{\infty} h(x) \cdot f(x) \, dx = f(0)$, for every function $f(x)$. Then the value of the definite integral $\int_{-\infty}^{\infty} h'(x) \cdot \sin x \, dx$ is

$ \int \frac{1}{x^{2}\left(x^{4}+1\right)^{3 / 4}} dx $ is equal to

$\int \frac{dx}{x^2(x^4 + 1)^{3/4}} = $

Evaluate the integral $\int \frac{x^2 + \cos^2 x}{1 + x^2} \operatorname{cosec}^2 x \, dx$,where $c$ is the constant of integration.

Integrate the function: $\frac{x+2}{\sqrt{x^{2}-1}}$