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:
1 liter of water
Step-by-step explanation:
If 80 % is acid that's means 4 liters of the 5 is acid. (0.8 * 5)
The remaining amount is 1
The number (answer) is 2592.
Check your answer:
(substitute the numbers to see if they will equal 2592: <span>2^5 is 32 and 9^2 is 81)</span><span>
Now subsitute it into A^B*C^D: 32*81 is 2592.</span>
Hi,
Work:
Equation;
1. Write division as fraction.
2. Evaluate the power of 10².
3. Reduce the fraction with 20.
4. Multiply.
5. Finally subtract and RESULT.
Hope this helps.
r3t40
