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

• marmot
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.
marmot

## 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.

Uh, the ratio of those two polynomials is a VERY SIMPLE THING. Can you find it? Factor them.

Try this :
5 + 10y^4 = 4 + 1 + 10y^4

after you get it, think of a crafty substitution

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.

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.

## 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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