Find the integral.
-$\int 4(2 x+5)^{3} d x$
A) $\frac{3}{4}(2 x+5)^{4}+$ C
B) $\frac{1}{2}(2 x+5)^{4}+C$
C) $\frac{3}{8}(2 x+5)^{4}+C$
D) $\frac{1}{4}(2 x+5)^{4}+C$

Question

Quizplus · Accepted Answer

The integral can be solved using substitution. Let $ u = 2x + 5 $, then $ du = 2dx $ or $ dx = \frac{1}{2}du $. The integral becomes $ \int 4u^3 \cdot \frac{1}{2} du = 2 \int u^3 du $. Integrating $ u^3 $ gives $ \frac{u^4}{4} $, so the result is $ 2 \cdot \frac{u^4}{4} = \frac{1}{2}u^4 + C $. Substituting back $ u = 2x + 5 $, we get $ \frac{1}{2}(2x+5)^4 + C $.

Find the Integral ∫4(2x+5)3dx\int 4(2 x+5)^{3} d x∫4(2x+5)3dx A) 34(2x+5)4+\frac{3}{4}(2 x+5)^{4}+43​(2x+5)4+ C B)

Find the Integral $\int 4(2 x+5)^{3} d x$ A) $\frac{3}{4}(2 x+5)^{4}+$ C
B)