The value of the integral $I = \int_0^1 \frac{1}{\sqrt{1+3\sqrt{x}}} dx$ is

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

$\int_1^4 |x - 2|dx$ is equal to

If $2f(x) + f\left(\frac{1}{x}\right) = x^2 + 1$, then $\int f(x) dx$ is: (Here C is an arbitrary constant)

$\int \dfrac{e^{7\log x}-e^{6\log x}}{e^{5\log x}-e^{4\log x}}\,dx$, $x>0$ and $x\ne 1$ is equal to (consider $\log x = \log_e x$)

$\int \frac{dx}{2\sin^2 x + 5\cos^2 x}$ is equal to

The integral I = $\int \frac{e^{5\log_e x} - e^{4\log_e x}}{e^{3\log_e x} - e^{2\log_e x}} dx$ is equal to