Find the indefinite integral.
$$\int \left( x ^ { 2 } + 4 x - 5 \right) ^ { 2 } ( 2 x + 4 ) d x$$
A) $- 2 \left( x ^ { 2 } + 4 x - 5 \right) ^ { 3 } + C$
B) $2 \left( x ^ { 2 } + 4 x - 5 \right) ^ { 3 } + C$
C) $\left( x ^ { 2 } + 4 x - 5 \right) ^ { 3 } + C$
D) $\frac { 1 } { 3 } \left( x ^ { 2 } + 4 x - 5 \right) ^ { 3 } + C$

Question

Quizplus · Accepted Answer

We can expand the integrand using the binomial formula or use the substitution $u = x^2 + 4x - 5$ to simplify the integral. We obtain:

\begin{align*}
\int (x^2 + 4x - 5)^2(2x+4)dx &= \int u^2(du) \
&= \frac{1}{3}u^3 + C \
&= \frac{1}{3}(x^2 + 4x - 5)^3 + C
\end{align*}

Therefore, the answer is D.

Find the Indefinite Integral ∫(x2+4x−5)2(2x+4)dx\int \left( x ^ { 2 } + 4 x - 5 \right) ^ { 2 } ( 2 x + 4 ) d x∫(x2+4x−5)2(2x+4)dx

Find the Indefinite Integral $\int \left( x ^ { 2 } + 4 x - 5 \right) ^ { 2 } ( 2 x + 4 ) d x$