$\int_{0}^{2a} f(x) \, dx = $

$\int \limits_{6}^{16} \frac{\log _{e} x^{2}}{\log _{e} x^{2}+\log _{e}\left(x^{2}-44 x+484\right)} d x$ is equal to:

Given $\int_{0}^{\frac{\pi}{2}} \frac{dx}{1 + \sin x + \cos x} = \ln 2$,then the value of the definite integral $\int_{0}^{\frac{\pi}{2}} \frac{\sin x}{1 + \sin x + \cos x} dx$ is equal to

$\int_{-1/24}^{1/24} \sec x \log \left(\frac{1-x}{1+x}\right) dx =$

$\int_{-\pi}^{\pi} (1-x^2) \sin x \cdot \cos^2 x \, dx$ is equal to:

If $I_1 = \int\limits_0^1 {{e^{ - x}}} {\cos ^2}x\,dx$,$I_2 = \int\limits_0^1 {{e^{ - {x^2}}}} {\cos ^2}x\,dx$ and $I_3 = \int\limits_0^1 {{e^{ - {x^3}}}} dx$; then