Find the integral using the indicated substitution.
$$\int ( 4 x + 3 ) ^ { 6 } d x , \quad u = 4 x + 3$$ Select the correct answer.
A) $\frac { 1 } { 28 } ( 4 x + 3 ) ^ { 7 } + C$
B) $6 ( 4 x + 3 ) ^ { 7 } + C$
C) $\frac { 1 } { 6 } ( 4 x + 3 ) ^ { 2 } + C$
D) $\frac { 1 } { 7 } ( 4 x + 3 ) ^ { 2 } + C$

Question

Quizplus · Accepted Answer

Using the substitution $u = 4x+3$, we have $du = 4dx$ or $dx = \frac{1}{4}du$. Thus, we can write the integral as

$$\int (4x+3)^6dx = \frac{1}{4}\int u^6du = \frac{1}{28}u^7 + C$$

Substituting back for $u$, we get

$$\int (4x+3)^6dx = \frac{1}{28}(4x+3)^7 + C$$

Option A is the correct answer.

Find the Integral Using the Indicated Substitution ∫(4x+3)6dx,u=4x+3\int ( 4 x + 3 ) ^ { 6 } d x , \quad u = 4 x + 3∫(4x+3)6dx,u=4x+3

Find the Integral Using the Indicated Substitution $\int ( 4 x + 3 ) ^ { 6 } d x , \quad u = 4 x + 3$