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:
39
Step-by-step explanation:
78/2 = 39
Change mixed fraction to improper fraction and also the second fraction has to be reciprocal
Ex- 3/8= 8/3
So now the problem is
13/8*8/3= 13/3 (because you cross divide) Now, turn into fraction
Divide
13 divided by 3= 4 1/3
So your final answer is 4 1/3
Answer: d
Step-by-step explanation: formula is 1/2bh 14 times 6 is 84 divided by 2 is 42
