Use differentiation to determine whether the integral formula is correct.
-$$\int 4 x ( 2 x + 7 ) ^ { 3 } d x = \frac { 1 } { 2 } x ^ { 2 } ( 2 x + 7 ) ^ { 4 } + C$$

Question

Quizplus · Accepted Answer

Differentiating $\frac { 1 } { 2 } x ^ { 2 } ( 2 x + 7 ) ^ { 4 } + C$ using the product rule and chain rule does not yield $4x(2x+7)^3$, indicating the integral formula is incorrect.

Use Differentiation to Determine Whether the Integral Formula Is Correct ∫4x(2x+7)3dx=12x2(2x+7)4+C\int 4 x ( 2 x + 7 ) ^ { 3 } d x = \frac { 1 } { 2 } x ^ { 2 } ( 2 x + 7 ) ^ { 4 } + C∫4x(2x+7)3dx=21​x2(2x+7)4+C

Use Differentiation to Determine Whether the Integral Formula Is Correct $\int 4 x ( 2 x + 7 ) ^ { 3 } d x = \frac { 1 } { 2 } x ^ { 2 } ( 2 x + 7 ) ^ { 4 } + C$