$\int \frac{dx}{e^x + e^{-x}} = $

The integral $\int \frac{1}{\sqrt[4]{(x-1)^{3}(x+2)^{5}}} dx$ is equal to : (where $C$ is a constant of integration)

$\int \frac{1}{x^{\frac{1}{2}}+x^{\frac{1}{3}}} \, dx =$

If $\int \frac{2 \sin 2x - 3 \cos x}{2 \sin^2 x - 3 \sin x + 4} dx = f(x) + c$ where $c$ is the constant of integration, then $f\left(\frac{\pi}{2}\right) - f(0) =$

If $\int \frac{\sin 2x \, dx}{\sin^4 x + \cos^4 x} = \tan^{-1}(f(x)) + c$,then $f\left(\frac{\pi}{3}\right) = $

$\int \frac{\sin x \, dx}{(a + b \cos x)^2} = $