\((\int \frac{\sin 7x}{\cos 9x \cos 2x} dx)\) is equal to
The solution of the equation \((\frac{dy}{dx} = \frac{1}{x+y+1})\) is
The value of
\[ \int_{0}^{\pi} |\sin^3 x| \, dx \]
is ______.
\(( \int_0^1 \log(x + 1) , dx = )\)
If
\[ A = \begin{bmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{bmatrix} \]
where
\[ a = 7^x,\quad b = 7^{7^x},\quad c = 7^{7^{7^x}} \]
then
\[ \int |A| \, dx \]
is equal to ______.