Question
If $t(x)=-\frac{8}{x+4}$, determine the antiderivative of $t(x)$. (Do not include the constant $C$ in your answer.)
Note: When entering natural log in your answer, enter lowercase LN as "In". There is no "natural log" button on the Alta keyboard.
Provide your answer below:
FEEDBACK
MORE INSTRUCTION
SUBMIT
Content attribution
Answer
Final Answer: The antiderivative of \(t(x)=-\frac{8}{x+4}\) is \(\boxed{-8\ln|x+4|}\).
Step 1 ：The antiderivative of a function is the function whose derivative is the given function. In this case, we need to find the antiderivative of \(t(x)=-\frac{8}{x+4}\).
Step 2 ：This is a simple case of finding the antiderivative of a function of the form \(\frac{1}{x}\), which is \(\ln|x|\).
Step 3 ：However, we have a constant and a shift in the function, which we need to account for.
Step 4 ：The antiderivative of \(-\frac{8}{x+4}\) is \(-8\ln|x+4|\).
Step 5 ：Final Answer: The antiderivative of \(t(x)=-\frac{8}{x+4}\) is \(\boxed{-8\ln|x+4|}\).
