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

Question

Quizplus · Accepted Answer

We can use differentiation to verify the integral:
\begin{align*}
\frac{d}{dx}\left(-\frac{1}{(x+1)^2}+Cight) &= \frac{d}{dx}\left(\frac{-1}{(x+1)^2}ight)+\frac{d}{dx}C \
&= \frac{2}{(x+1)^3}+0 \
&= \frac{2}{(x+1)^3}
\end{align*}
This matches the integrand, so the integral formula is correct.

Use Differentiation to Determine Whether the Integral Formula Is Correct ∫2(x+1)3dx=−1(x+1)2+C\int \frac { 2 } { ( x + 1 ) ^ { 3 } } d x = - \frac { 1 } { ( x + 1 ) ^ { 2 } } + C∫(x+1)32​dx=−(x+1)21​+C

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