$\int\left[\sin^2(2x)\cos^3(2x)\right]dx=\int\left[\sin^2(2x)\cos^2(2x)\cos(2x)\right]dx\\\\\text{Use the trigonometric identity}\sin^2(x)+\cos^2(x)=1\to\cos^2(x)=1-\sin^2(x)\\\\=\int\left\{\sin^2(2x)[1-\sin^2(2x)]\cos(2x)\right\}dx\\\\\text{substitute}\ \sin2x=t\ \to\ 2\cos2x\ dx=dt\ \to\ \cos2x\ dx=\dfrac{1}{2}\ dt\\\\=\dfrac{1}{2}\int\left[t^2(1-t^2)\right]dt=\dfrac{1}{2}\int(t^2-t^4)dt=\dfrac{1}{2}\left(\dfrac{1}{3}t^3-\dfrac{1}{5}t^5\right)+C$

$=\dfrac{1}{2}\left(\dfrac{1}{3}\sin^3(2x)-\dfrac{1}{5}\sin^5(2x)\right)+C$

4 0

3 years ago

If the conversion rate for Swiss francs is 1.68 francs = 1 U.S. dollar, then how many Swiss francs can be exchanged for $79.00 i

Likurg_2 [28]

If one U.S. dollar is as much as 1.68 Swiss francs, then 79,00 U.S. dollars will be as much as 79,00 * 1,68, which is 132,72 Swiss francs.

I hope it will help :)

3 0

3 years ago

A car averages 30 miles of driving for 1 gallon of gas if the car holds 12 gallons how many times will we have to fill up his ga

icang [17]

Answer:

7 times

Step-by-step explanation:

30 miles per 1 gallon

Car holds 12 gallons

30x12=360

2520/360=7

3 0

3 years ago

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