Value of $\int (e^{2\log x} + e^{x\log 2} + e^{2\log 2})dx$ is

The value of $\int_0^1 [\log x - \log(1-x)] dx$ is

If the integral $I = \int \left[log_e(log_e x)^2 + \frac{a}{log_e x}\right] dx = x log_e(log_e x)^2 + C$, where C is constant of integration. Then the value of $a$ is:

$\int_{0}^{\pi} \frac{e^{\cos x}}{e^{\cos x} + e^{-\cos x}} dx =$

The value of $\int_0^1 \log_e\left(\frac{1}{x} - 1\right)dx$ is:

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\sin|x| + \cos|x|)dx$, is equal to:

$\int \left(\frac{1}{log_e t} - \frac{1}{(log_e t)^2}\right) dt$ is equal to