Evaluate the integral using Partial fraction decomposition (PLEASE SHOW EVERY STEPS: the dummy decomposition form, specific decomposition form, and the linear system that must be solved to get from one to the other. Make sure to Label every step and explain the process

The integral (-t^2+33t+18)/(t^3-9t)dt

2. The initial composition of 200 kg organic material to be decomposed is given by C. HON. After 8 weeks of decomposition, the residual organic matter is estimated to be C, H. ON with 95 kg material remains. Determine the amount of oxygen involved in the decomposition process.9.23 The rate law for the decomposition of ozone to molecular oxygen (203 - 302) is [0312 rate = k [O2] The mechanism proposed for this process is KI 03 - 0+ 02 K- 1 O +03 k2 202Solve the following system of linear equations using LU decomposition. Show each step including the decomposition process, forward and backward substitutions, and verification of solutions. (1) X1 + X2 + X3 = 13, (11) X1 - X2 + X3 = 6, (Ill) X1 + X2 - X3 = -3