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ainster31
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Homework Statement
Homework Equations
The Attempt at a Solution
How did they go from the first step in the blue to the second step in the blue?
I tried integration by parts but that didn't work.
How to perform an integral with a polynomial and a radical?
- Thread starter ainster31
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- Integral Polynomial Radical
In summary, the student is struggling with a problem involving integration and attempted both integration by parts and substitution methods. They eventually discovered that u substitution with u=x^(2/3) was the correct approach after taking a factor of x^(-2/3) outside of the radical. They also mention accidentally deleting their first post while editing.
How did they go from the first step in the blue to the second step in the blue?
I tried integration by parts but that didn't work.
- #2
ainster31
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Dick said:
I suck at integration... that was such an easy one. =[
I tried for several papers to do substitution ##u=x^{1/3}##.
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Dick
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ainster31 said:Homework Statement
Homework Equations
The Attempt at a Solution
How did they go from the first step in the blue to the second step in the blue?
I tried integration by parts but that didn't work.
They took a factor of x^(-2/3) outside of the radical where it becomes x^(-1/3). Then just u substitution u=x^(2/3). Sorry, I accidentally deleted my first post while editing. So this is out of order.
Related to How to perform an integral with a polynomial and a radical?
1. How do I determine the limits of integration when performing an integral with a polynomial and a radical?
To determine the limits of integration, you need to set the polynomial and radical equal to each other and solve for the variable of integration. The resulting values will be your lower and upper limits.
2. What is the general process for performing an integral with a polynomial and a radical?
The general process for performing an integral with a polynomial and a radical is to first simplify the expression by combining like terms and factoring out any common factors. Then, use the power rule to integrate the polynomial term, and the substitution method to integrate the radical term.
3. Can I use any integration technique for a polynomial and a radical, or are there specific methods for this type of integral?
While there are various integration techniques, the most efficient method for integrating a polynomial and a radical is the substitution method. This involves substituting the radical expression with a new variable, simplifying the resulting polynomial, and then using the power rule to integrate.
4. Is it possible to have multiple radicals in a polynomial and still perform an integral?
Yes, it is possible to have multiple radicals in a polynomial and still perform an integral. The key is to simplify the expression by combining like terms and factoring out any common factors, and then using the substitution method to integrate each radical term individually.
5. Are there any special cases to consider when performing an integral with a polynomial and a radical?
One special case to consider is when the polynomial contains a radical in its denominator. In this case, you will need to use the method of partial fractions before integrating the expression. Additionally, if the polynomial and the radical do not have a common factor, the substitution method may not work and you will need to use other techniques such as integration by parts.
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