Use differentiation to determine whether the integral formula is correct.
-$$\int \sec ^ { 2 } \left( \frac { x - 6 } { 5 } \right) d x = - 5 \cot \left( \frac { x - 6 } { 5 } \right) + C$$

Question

Quizplus · Accepted Answer

Differentiating $-5\cot\left(\frac{x-6}{5}\right) + C$ gives $\sec^2\left(\frac{x-6}{5}\right) \cdot \frac{1}{5}$, not $\sec^2\left(\frac{x-6}{5}\right)$, indicating an error in the integral formula.

Use Differentiation to Determine Whether the Integral Formula Is Correct ∫sec⁡2(x−65)dx=−5cot⁡(x−65)+C\int \sec ^ { 2 } \left( \frac { x - 6 } { 5 } \right) d x = - 5 \cot \left( \frac { x - 6 } { 5 } \right) + C∫sec2(5x−6​)dx=−5cot(5x−6​)+C

Use Differentiation to Determine Whether the Integral Formula Is Correct $\int \sec ^ { 2 } \left( \frac { x - 6 } { 5 } \right) d x = - 5 \cot \left( \frac { x - 6 } { 5 } \right) + C$