Question

exercises 1.5 substitution
score: 100/170 answered: 10/17
question 14
evaluate the indefinite integral
\\(\int 9\sin^3 x \cos x dx =\\)
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Explanation:

Step1: Choose substitution variable

Let $u = \sin x$

Step2: Compute derivative of u

$\frac{du}{dx} = \cos x \implies du = \cos x dx$

Step3: Rewrite integral in terms of u

$\int 9u^3 du$

Step4: Factor out constant and integrate

$9 \cdot \frac{u^4}{4} + C = \frac{9}{4}u^4 + C$

Step5: Substitute back $u=\sin x$

$\frac{9}{4}\sin^4 x + C$

Answer:

$\frac{9}{4}\sin^4 x + C$