The value of $\int_{-a}^a f(x)dx$ where $f(x) = \frac{7^x}{1+7^x}$ is:

$\int \frac{x^2 - 4}{(x+2)(x-1)(x-3)} dx =$

$\int \left(\frac{\cos x - \sin x}{1 + \sin 2x}\right) dx$ is equal to

If $\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C$, where C is constant of integration, then $f(x)$ is

$\int \frac{e^{2x} - 1}{e^{2x} + 1} dx =$

The value of $\int_{0}^{\pi/2} \frac{\tan^7 x}{\cot^7 x + \tan^7 x} dx$ is

$\int (e^{x\log a} + e^{a\log x}) dx$ is equal to (where $a > 1$)