A) x+6
B)3x
C)x/7
D)4-5x
E)x^2-2
F)2X+16
The answer is (1/2)xe^(2x) - (1/4)e^(2x) + C
Solution:
Since our given integrand is the product of the functions x and e^(2x), we can use the formula for integration by parts by choosing
u = x
dv/dx = e^(2x)
By differentiating u, we get
du/dx= 1
By integrating dv/dx= e^(2x), we have
v =∫e^(2x) dx = (1/2)e^(2x)
Then we substitute these values to the integration by parts formula:
∫ u(dv/dx) dx = uv −∫ v(du/dx) dx
∫ x e^(2x) dx = (x) (1/2)e^(2x) - ∫ ((1/2) e^(2x)) (1) dx
= (1/2)xe^(2x) - (1/2)∫[e^(2x)] dx
= (1/2)xe^(2x) - (1/2) (1/2)e^(2x) + C
where c is the constant of integration.
Therefore,
∫ x e^(2x) dx = (1/2)xe^(2x) - (1/4)e^(2x) + C
Answer:
tôi không hiểu bạn nói gì
Step-by-step explanat ion :
1 ray DE
2 ray ED
3 ray EC
4 ray CE
5 ray DC
6 ray CD
7 ray CA
8 ray AC
9 ray CB
10 ray BC
11 ray AB
12 ray BA
66 x 3 = 198
198 + 2 = 200
200 / 3
As an improper fraction, anyway. 66 2/3 is already *technically* a fraction.
