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

Integrate the function $\left(x^{3}-1\right)^{\frac{1}{3}} x^{5}$.

$\int \frac{2 t+1}{t^2+t+1} d t=$

$\int \frac{\sin 2x}{\sin^4 x + \cos^4 x} \, dx = $

Consider the following statements:
Assertion $(A):$ $\frac{1}{x^2 + a^2}$ can be integrated by a substitution $x = a \tan \theta$.
Reason $(R):$ Because all integrands are integrated by the method of substitution only.
Which of the following is correct?

$\int \frac{e^x dx}{\sqrt{a + b e^x}} = $