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:
3x + 4 = 12
Step-by-step explanation:
plus = +
equal = =
but if you were looking for the answer to the equation
3x + 4 = 12
3x = 12 - 4 (the symbol changes bc i switched it to the other side)
3x = 8
x = 8/3
~batmans wife dun dun dun.....
AFB, the sides are similar
3:13 - 1:00 = 2:13
2:13 - 0:37 = 1:36
1:36 is your answer.
Glad I could help, and good luck!
AnonymousGiantsFan
