Question

exercises 1.5 substitution
score: 20/170 answered: 2/17
question 3
evaluate the integral
\\(\int (2x + 4) (x^2 + 4x + 9)^5 dx\\)
by making the substitution \\(u = x^2 + 4x + 9\\).
\\(\square\\) + c
note: your answer should be in terms of \\(x\\) and not \\(u\\).
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Explanation:

Step1: Compute derivative of $u$

$\frac{du}{dx} = 2x + 4 \implies du = (2x+4)dx$

Step2: Substitute $u$ and $du$ into integral

$\int u^5 du$

Step3: Integrate power function

$\frac{u^{5+1}}{5+1} = \frac{u^6}{6}$

Step4: Substitute back $u=x^2+4x+9$

$\frac{(x^2+4x+9)^6}{6}$

Answer:

$\frac{(x^2+4x+9)^6}{6} + C$