Question: "Make the given substitutions to evaluate the indefinite..."

foass77W

Answered question

2021-11-10

Make the given substitutions to evaluate the indefinite integral.

\int 2 {(2 x + 4)}^{2} d x

Szeteib

Skilled2021-11-11Added 102 answers

Step 1
To evaluate integral:

\int 2 {(2 x + 4)}^{2} d x

.
Let substitute u=2x+4
Differentiating with respect to x,

\frac{d u}{d x} = \frac{d}{d x} (2 x + 4)

\frac{d u}{d x} = 2 \cdot 1 + 0

\frac{d u}{d x} = 2

du=2dx
Step 2
Substituting the value, we get

\int 2 {(2 x + 4)}^{2} d x = \int u^{2} d u

= \frac{u^{2 + 1}}{2 + 1} + C

= \frac{u^{3}}{3} + C

Put back u=2x+4

\int 2 {(2 x + 4)}^{2} d x = \frac{{(2 x + 4)}^{3}}{3} + C

Hence, required answer is

\frac{{(2 x + 4)}^{3}}{3} + C

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