Answer:
-2x+4r = 4 i think
Step-by-step explanation:
Answer:
There are (14 - 8) daisies = 6 daisies
roses / daises = 8 / 6 = 4 / 3
flowers / daises = 14 / 6 = 7 / 3
that would be 20 miles per hour. If in 8 hours you're going 160, then divide 160 by 8 and you'd get 20. Each hour is 20 miles. or 8 times 20 is 160. Your answer is 20 miles per hour
Answer:
.
Step-by-step explanation:
We have been given an indefinite integral
. We are asked to find the value of the integral using integration by parts.
Let
,
.
Now, we will find du and v as shown below:
![\frac{du}{dx}=\frac{d}{dx}(\text{ln}(x))](https://tex.z-dn.net/?f=%5Cfrac%7Bdu%7D%7Bdx%7D%3D%5Cfrac%7Bd%7D%7Bdx%7D%28%5Ctext%7Bln%7D%28x%29%29)
![\frac{du}{dx}=\frac{1}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bdu%7D%7Bdx%7D%3D%5Cfrac%7B1%7D%7Bx%7D)
![du=\frac{1}{x}dx](https://tex.z-dn.net/?f=du%3D%5Cfrac%7B1%7D%7Bx%7Ddx)
![v=\frac{x^{3+1}}{3+1}=\frac{x^{4}}{4}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bx%5E%7B3%2B1%7D%7D%7B3%2B1%7D%3D%5Cfrac%7Bx%5E%7B4%7D%7D%7B4%7D)
Upon substituting our values in integration by parts formula, we will get:
![\int \:x^3\:\text{ln}\:(x)\:dx=\text{ln}(x)*\frac{x^4}{4}-\int\: \frac{x^4}{4}*\frac{1}{x}dx](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Ctext%7Bln%7D%28x%29%2A%5Cfrac%7Bx%5E4%7D%7B4%7D-%5Cint%5C%3A%20%5Cfrac%7Bx%5E4%7D%7B4%7D%2A%5Cfrac%7B1%7D%7Bx%7Ddx)
![\int \:x^3\:\text{ln}\:(x)\:dx=\frac{\text{ln}(x)x^4}{4}-\int\: \frac{x^3}{4}dx](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Cfrac%7B%5Ctext%7Bln%7D%28x%29x%5E4%7D%7B4%7D-%5Cint%5C%3A%20%5Cfrac%7Bx%5E3%7D%7B4%7Ddx)
![\int \:x^3\:\text{ln}\:(x)\:dx=\frac{\text{ln}(x)x^4}{4}-\frac{1}{4}\int\: x^3dx](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Cfrac%7B%5Ctext%7Bln%7D%28x%29x%5E4%7D%7B4%7D-%5Cfrac%7B1%7D%7B4%7D%5Cint%5C%3A%20x%5E3dx)
![\int \:x^3\:\text{ln}\:(x)\:dx=\frac{\text{ln}(x)x^4}{4}-\frac{1}{4}*\frac{x^{3+1}}{3+1}+C](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Cfrac%7B%5Ctext%7Bln%7D%28x%29x%5E4%7D%7B4%7D-%5Cfrac%7B1%7D%7B4%7D%2A%5Cfrac%7Bx%5E%7B3%2B1%7D%7D%7B3%2B1%7D%2BC)
![\int \:x^3\:\text{ln}\:(x)\:dx=\frac{\text{ln}(x)x^4}{4}-\frac{1}{4}*\frac{x^4}{4}+C](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Cfrac%7B%5Ctext%7Bln%7D%28x%29x%5E4%7D%7B4%7D-%5Cfrac%7B1%7D%7B4%7D%2A%5Cfrac%7Bx%5E4%7D%7B4%7D%2BC)
![\int \:x^3\:\text{ln}\:(x)\:dx=\frac{\text{ln}(x)x^4}{4}-\frac{x^4}{16}+C](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Cfrac%7B%5Ctext%7Bln%7D%28x%29x%5E4%7D%7B4%7D-%5Cfrac%7Bx%5E4%7D%7B16%7D%2BC)
Therefore, our required integral would be
.