Question 14

Evaluate the indefinite integral
$\int 6 \sin^{4} v \cos v d v =$

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Answer

Finally, the indefinite integral $\int 6 \sin^{4} v \cos v d v$ is $1.2 \sin^{5} v + C$ where C is the constant of integration.

Steps

Step 1 ：Let's evaluate the indefinite integral $\int 6 \sin^{4} v \cos v d v$ .

Step 2 ：We can rewrite the integral as $6 / 5 \times \int d u$ .

Step 3 ：Here, $u = \sin (v)^{5}$ and $d u = 5 \sin (v)^{4} \cos (v) d v$ .

Step 4 ：Substituting these values, the integral simplifies to $1.2 \sin (v)^{5}$ .

Step 5 ：Finally, the indefinite integral $\int 6 \sin^{4} v \cos v d v$ is $1.2 \sin^{5} v + C$ where C is the constant of integration.