Solving the Integral: A Step-by-Step Guide

  • Thread starter tommy_ita
  • Start date
  • Tags
    Integral
In summary, the conversation is about solving an integral using integration by parts and substitution. The integral in question is ∫x³dx /(x + 5), and the conversation includes hints and steps on how to solve it.
  • #1
tommy_ita
6
0
Can someone solve this integral as the answer, please? I'm sure it is easy for you:

see attached picture, please! :)
 

Attachments

  • tommy_ita.JPG
    tommy_ita.JPG
    4.2 KB · Views: 325
Physics news on Phys.org
  • #2
What have you attempted? Use integration by parts.
 
  • #3
hi,

integration by parts seems to be right!

I just don't get through the first steps... help! ;)
 
  • #4
What is formula for integration by parts? What should you let u and dv be?
 
  • #5
Defennder said:
What is formula for integration by parts? What should you let u and dv be?

S u dv = uv - S v du

u= ln(x+5)
dv= (x^3)/3


I just don't know how to solve it if where there is an addition after ln(...)

thanks
 
  • #6
dv isn't x^3/3, that's v.

So you need to find du now. Or du/dx. Check out the derivative of function ln(f(x)). Then plug that into the formula.
 
  • #7
thanks
 
  • #8
hi, now I'm there

ln(x+5) x^3/3 - 1/3 S x^3 1/(x+5) dx

how can i solve this integral?

S x^3 1/(x+5) dx


thank you again!
 
  • #9
Welcome to PF!

tommy_ita said:
hi, now I'm there

ln(x+5) x^3/3 - 1/3 S x^3 1/(x+5) dx

how can i solve this integral?

Hi tommy_ita! Welcome to PF! :smile:

(have an integral: ∫ and a cubed: ³)

You mean ∫x³dx /(x + 5) …

either long-division to get a constant/(x + 5) plus a quadratic,

or substitute y = x + 5, integrate, and substitute back again. :smile:

(in hindsight, making that substitution before integrating by parts might have been simpler :wink:)
 
  • #10
hi tiny-tim,

thanks for the ∫ :D


unfortunately, I am not able to find the solution. Could you help me by doing the integral step-by-step?
that'd be very nice

∫x³dx /(x + 5) =
 
  • #11
tommy_ita said:
hi tiny-tim,

thanks for the ∫ :D


unfortunately, I am not able to find the solution. Could you help me by doing the integral step-by-step?
that'd be very nice

∫x³dx /(x + 5) =

Hi tommy_ita! :smile:

When in doubt. use the obvious substitution, in this case:

y = x + 5, dy = dx,

∫x³dx /(x + 5) = ∫(y - 5)³dy /y = ∫(Ay² + By + C + (D/y))dy …

and you can fill in the rest yourself, can't you? :smile:
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve in a graph. It is used to solve problems in calculus and is an important tool in many areas of science and engineering.

2. Why do we need to solve integrals?

Integrals are used to solve a variety of problems, such as calculating areas, volumes, and distances. They are also used to find the derivatives of a function, which is important in understanding the behavior of a system over time.

3. Can anyone solve an integral?

While anyone can learn how to solve integrals with the right knowledge and practice, it does require a strong understanding of calculus and mathematical concepts. It is a common topic in college-level math courses and may require guidance from a teacher or tutor.

4. Who is typically able to solve integrals?

Individuals with a strong background in mathematics, particularly in calculus, are typically able to solve integrals. This includes mathematicians, engineers, physicists, and other scientists who use calculus in their work.

5. How can I learn to solve integrals?

There are many resources available for learning how to solve integrals, including textbooks, online tutorials, and classes. It is important to have a strong foundation in calculus before attempting to learn how to solve integrals.

Similar threads

  • Calculus and Beyond Homework Help
Replies
7
Views
640
  • Calculus and Beyond Homework Help
Replies
1
Views
804
  • Calculus and Beyond Homework Help
Replies
9
Views
790
  • Calculus and Beyond Homework Help
Replies
5
Views
659
  • Calculus and Beyond Homework Help
Replies
24
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
738
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
1K
Back
Top