Integration by Parts: Solve x^2exp(-3x)dx

In summary, The conversation is about using integration by parts to solve a question involving the integral of *integral sign* x^2 . exponential ^ -3x . dx. The participants discuss the use of the tabular method and the need for an arbitrary constant in the solution. One participant also provides a link to further explanation of the tabular method.
  • #1
cogs24
30
0
hi guys
just doing some revision and I am stuck on this question

*integral sign* x^2 . exponential ^ -3x . dx

I know i have to use integration by parts, but i just can't seem to get it out
any ideas?
thanx
 
Physics news on Phys.org
  • #2
HINT:Take [tex]dv=e^{-3x} \ dx [/tex] and [tex] u=x^2 [/tex].

U'll figure out what to do next.

Daniel.
 
  • #3
but, what is the integral of exponential ^ -3x?
 
  • #4
is it -1/3 *exponential* ^ -3x?
 
  • #5
Yes,as you can check by differentiation.

Daniel.
 
  • #6
The tabular method would work great on this question. Are you familiar with this?
 
  • #7
ok, once i sub u, du, v and dv into the integral by parts formula, i have to assign, u and dv again to:
-1/3 exponential ^ -3x and 2x

so is dv assigned to the exponential again, like in the first case?
 
  • #8
no, i am not aware of the tabular method, sorry
 
  • #9
ok, I've got my answer, unfortunately i don't kow if its right, we don't get solutions for this exercise

-1/3 *exponential* ^ -3x . x^2 - 1/9*exponential*^-3x . 2x - 2/27*exponential*^-3x
 
  • #10
Maple agrees, good job.
 
  • #11
Surely,you must add an arbitrary constant wrt "x" to your solution.

Daniel.
 
  • #12
arbitary constant would be + c
 
  • #13
In case you were interested in this method, http://marauder.millersville.edu/~bikenaga/calculus/parts/partspf.html is a link to the explanation. If one of the two terms will eventually differentiate to zero, this method is much less time consuming.

Jameson
 
Last edited by a moderator:
  • #14
i see, thanks for that link, i will probably apply this method from now on
 

FAQ: Integration by Parts: Solve x^2exp(-3x)dx

1. What is integration by parts?

Integration by parts is a method used in calculus to solve integrals that involve the product of two functions. It involves breaking down the integral into two parts and using the product rule of differentiation to simplify it.

2. How do you know when to use integration by parts?

You should use integration by parts when you have an integral that involves a product of two functions and you are unable to solve it using other methods such as substitution or trigonometric identities.

3. What are the steps to solve an integral using integration by parts?

The steps to solve an integral using integration by parts are:1. Identify the two functions in the integral and label them as u and v.2. Use the product rule to find the derivative of u and the antiderivative of v.3. Substitute these values into the integration by parts formula: ∫u dv = uv - ∫v du.4. Simplify the integral on the right side of the equation.5. Repeat the process until the integral can be solved.

4. How do I apply integration by parts to solve x^2exp(-3x)dx?

To solve x^2exp(-3x)dx using integration by parts, you would first identify u as x^2 and dv as exp(-3x)dx. Then, use the product rule to find the derivative of u and the antiderivative of v. Substitute these values into the integration by parts formula and simplify the resulting integral. Repeat the process until the integral can be solved.

5. Are there any tips for solving integrals using integration by parts?

One tip for solving integrals using integration by parts is to choose u as the function that becomes simpler when differentiated. This will make the process easier and may result in a simpler integral to solve. Additionally, it may be helpful to practice and become familiar with the integration by parts formula and its application to different types of integrals.

Similar threads

B Integration by parts of inverse sine, a solved exercise, some doubts...
Replies
4
Views
2K
B Integration by Parts, an introduction I get confused with
Replies
2
Views
2K
I Did Math DF's integral calculator make a glaring mistake?
Replies
8
Views
1K
A Non solvable integral? (dx/dt)^2 dt
Replies
3
Views
2K
I Solving the Difficult Integral ##\int_0^{\infty} x^{n+1} e^{-x} \sin(ax) dx##
Replies
5
Views
2K
B Why don't we account for the constant in integration by parts?
Replies
16
Views
3K
MHB Differentiation under integral sign
Replies
4
Views
2K
I Curiosity: there exists the exponential integral?
Replies
3
Views
1K
I Gaussian integral by differentiating under the integral sign
Replies
19
Views
3K
A A question about a complex integral
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top