Duration: 11:25

13 views

1

If \( A \) is square matrix and \( e^{A} \) is defined as
P \( e^{A}=I+A+\frac{A^{2}}{2 !}+\frac{A^{3}}{3 !}+\cdots=\frac{1}{2}\left[\begin{array}{ll}f(x) & g(x) \\ g(x) & f(x)\end{array}\right] \), where

W \( A=\left[\begin{array}{ll}x & x \\ x & x\end{array}\right] \) and \( 0x1, I \) is an identity matrix.
\( \int \frac{g(x)}{f(x)} d x \) is equal to
(1) \( \log \left(e^{x}+e^{-x}\right)+c \)
(2) \( \log \left|e^{x}-e^{-x}\right|+c \)
(3) \( \log \left|e^{2 x}-1\right|+c \)
(4) none of these
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live