Question

exercises 1.5 substitution
score: 50/170 answered: 5/17
question 6
evaluate the indefinite integral.
\\(\int 4 \sin^6(x) \cos(x) dx = \\) \\(\square\\) + c
question help: video message instructor
submit question jump to answer

Explanation:

Step1: Choose substitution variable

Let $u = \sin(x)$

Step2: Find derivative of $u$

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

Step3: Rewrite integral in terms of $u$

$\int 4u^6 du$

Step4: Apply power rule for integration

$4 \cdot \frac{u^{6+1}}{6+1} = 4 \cdot \frac{u^7}{7}$

Step5: Substitute back $u=\sin(x)$

$\frac{4}{7}\sin^7(x)$

Answer:

$\frac{4}{7}\sin^7(x)$