overall accuracy: 86.5% record: 27 score: 27 ∫ 1/(3 - x) dx equals 1/((3 - x)^2) + c - ln|3 - x| + c ln|3…

overall accuracy: 86.5% record: 27 score: 27 ∫ 1/(3 - x) dx equals 1/((3 - x)^2) + c - ln|3 - x| + c ln|3 - x| + c - 1/((3 - x)^2) + c high score board: overall you must have at least 100 to be on the board. # name record

overall accuracy: 86.5% record: 27 score: 27 ∫ 1/(3 - x) dx equals 1/((3 - x)^2) + c - ln|3 - x| + c ln|3 - x| + c - 1/((3 - x)^2) + c high score board: overall you must have at least 100 to be on the board. # name record

Answer

Explanation:

Step1: Use substitution method

Let $u = 3 - x$, then $du=-dx$.

Step2: Rewrite the integral

The integral $\int\frac{1}{3 - x}dx$ becomes $-\int\frac{1}{u}du$.

Step3: Integrate $\frac{1}{u}$

We know that $\int\frac{1}{u}du=\ln|u|+C$. So $-\int\frac{1}{u}du =-\ln|u|+C$.

Step4: Substitute back $u = 3 - x$

We get $-\ln|3 - x|+C$.

Answer:

$-\ln|3 - x|+C$