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

$\int \frac{1}{x^2+4x+8}dx$ is equal to (Where C is an arbitrary constant)

$\int e^{-x}(\cot x + \cosec^2 x)dx =$

The value of the integral $I=\displaystyle\int\dfrac{e^x(x-2)}{(x+1)^4}dx$ is, [$C$ is an arbitrary constant]

Match the LIST-I with LIST-II (where $[x]$ denotes greatest integer function)

Choose the correct answer from the options given below:

If $f(x)$ and $g(x)$ are continuous functions in [0, a] such that $f(x) = f(a - x)$ and $g(x) + g(a - x) = a$ then $\int_{0}^{a} f(x)g(x)dx =$

If $\int e^{3\log x}(x^4+1)^{-1}dx = \frac{m}{n}\log(x^4+1)+C$, where C is an arbitrary constant, $m$ and $n$ are positive integers such that g.c.d $(m,n)=1$, then $(4m^2+n^2)$ is equal to