Integrating Int((5+10y^4)dy/(y+2y^5)) - A Step-by-Step Guide

In summary, the conversation discusses solving the integral int((5+10y^4)dy/(y+2y^5)) using integration, substitution, and partial fractions. The participants suggest factoring and canceling a common factor before using a crafty substitution to solve the integral. Eventually, the solution is found and the conversation ends with gratitude.
  • #1
marmot
55
1

Homework Statement



I want to deal with this int((5+10y^4)dy/(y+2y^5))

Homework Equations



integration, substitution, partial fractions?


The Attempt at a Solution



I tried a bunch of random things. I think it hs to do with substitution because if I make u=y+2y^5, du/dy=1+10y^4 which is strikingly similar to the numerator, so there must be a cancellation. this integral is part of a dif equation, but i can't see to go past this! i know for sure this is the correct set up because i used my calculator to integrate and it solved the differential equation.
 
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  • #2
Uh, the ratio of those two polynomials is a VERY SIMPLE THING. Can you find it? Factor them.
 
  • #3
Try this :
5 + 10y^4 = 4 + 1 + 10y^4

after you get it, think of a crafty substitution
 
  • #4
aostraff said:
Try this :
5 + 10y^4 = 4 + 1 + 10y^4

after you get it, think of a crafty substitution

Think of a crafty cancellation before you do the crafty substitution.
 
  • #5
jesus i feel like a complete retard. i hate when i don't get something as obvious.i factored both and canceled that nasty factor and then everything went smooth, thanks a bunch gentlemen.
 

Related to Integrating Int((5+10y^4)dy/(y+2y^5)) - A Step-by-Step Guide

1. What is the purpose of integrating (5+10y^4)/(y+2y^5)?

The purpose of integrating (5+10y^4)/(y+2y^5) is to find the antiderivative of the given function. This is useful in solving various problems in physics, engineering, and other scientific fields.

2. What are the steps involved in integrating (5+10y^4)/(y+2y^5)?

The steps involved in integrating (5+10y^4)/(y+2y^5) are:

  1. Expand the denominator
  2. Rewrite the integral as a sum of two fractions
  3. Integrate each fraction separately
  4. Combine the two integrals using the power rule

3. Why is it important to follow the steps in order when integrating (5+10y^4)/(y+2y^5)?

Following the steps in order ensures that the integral is solved correctly and accurately. Skipping steps or doing them in the wrong order can lead to incorrect results.

4. What are some common mistakes to avoid when integrating (5+10y^4)/(y+2y^5)?

Some common mistakes to avoid when integrating (5+10y^4)/(y+2y^5) include:

  • Forgetting to expand the denominator
  • Incorrectly rewriting the integral as a sum of fractions
  • Making errors in integrating each fraction separately
  • Forgetting to combine the integrals using the power rule

5. Can the steps for integrating (5+10y^4)/(y+2y^5) be applied to other integrals?

Yes, the steps for integrating (5+10y^4)/(y+2y^5) can be applied to other integrals as well. These steps are general and can be used to solve integrals of various functions.

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