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:
B
Step-by-step explanation:
i hope it helps
#CarryOnLearning
Answer:
Step-by-step explanation:
the answers 3452
Answer: -2
I'm not so sure what it means by slope, but because I saw a pattern between x and y (it decreases by 2 every x value and decreases by 4 every TWO x values) values so I would pick -2. BUT I don't know if the answer is -4.
Step-by-step explanation:
Answer:
X = -5
Step-by-step explanation:
3X=-15
Lets solve the equation for x. We will isolate x by dividing each side by 3
3X/3 = -15/3
X = -5
