Problem
Question 11 Evaluate the indefinite integral. \[ \int \frac{4}{(t+4)^{2}} d t=\square+c \] Question Help: $\square$ Video $B$ Written Example Submit Question Jump to Answer
Solution
Step 1 ：Let's set \(u = t + 4\). Then, \(du = dt\).
Step 2 ：Substitute these into the integral: \(\int \frac{4}{u^{2}} du\).
Step 3 ：This integral can be rewritten as: \(4 \int u^{-2} du\).
Step 4 ：Now we can apply the power rule for integration: \(4 \cdot \frac{1}{-1} u^{-1} + C\).
Step 5 ：Simplify this to: \(-4u^{-1} + C\).
Step 6 ：Finally, substitute \(t + 4\) back in for \(u\) to get the answer in terms of \(t\): \(-4/(t + 4) + C\).
Step 7 ：\(\boxed{-4/(t + 4) + C}\) is the solution to the integral.
