Solving ∫(52x^7/2-66x^5/2+22^3/2)/sqrt(x) - Help Needed!

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In summary, the conversation discusses the method for solving the integration of a fraction with a radical expression in the numerator. The recommended approach is to split up the fraction and simplify the powers of x first. It is also noted that \sqrt{x}=x^{\frac{1}{2}} and a term in the numerator may have been written incorrectly as 22^3/2 instead of 22x^{\frac{3}{2}}.
  • #1
Superposed_Cat
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Hi all, I am attempting to learn calculus in my spare time. Very short question. What rule do you use to solve ∫(52x^7/2-66x^5/2+22^3/2)/sqrt(x)? Could you please walk me through it. sorry I didn't use LaTex, I don't know it.
 
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  • #2
Split up the fraction, and simplify the powers of x first.
 
  • #3
arildno said:
Split up the fraction, and simplify the powers of x first.
what do you mean? I'm a total noob. How would I go about doing that?
 
Last edited:
  • #4
If you have a fraction (a+b+c)/d, you may write it as a/d+b/d+c/d

Also, remember that [itex]\sqrt{x}=x^{\frac{1}{2}}[/itex]

A question:
You have a term in your numerator, 22^3/2.
Should that have been: [itex]22x^{\frac{3}{2}}[/itex]?
 
  • #5
yes and thanks.
 

FAQ: Solving ∫(52x^7/2-66x^5/2+22^3/2)/sqrt(x) - Help Needed!

1. What is the process for solving this integral?

The first step in solving this integral is to simplify the expression inside the parentheses by factoring out the common term of 22^(3/2). This will result in the expression (52x^7/2-66x^5/2+22^(3/2))(1/sqrt(x)). From there, you can use the power rule and the constant multiple rule to integrate each term separately. Once each term has been integrated, you can combine them to get the final solution.

2. Is there a specific method or formula to use for solving this type of integral?

Yes, there are several methods that can be used for solving integrals. In this case, the power rule and the constant multiple rule are the most applicable. However, depending on the complexity of the integral, other methods such as substitution or integration by parts may also be used.

3. How do I know which variable to use for integration?

In this integral, the variable to use for integration is x. This is because the expression inside the parentheses is in terms of x, and the integral is taken with respect to x. Generally, the variable for integration will be specified or implied in the problem or equation.

4. Can I use a calculator to solve this integral?

Yes, you can use a calculator to solve this integral. However, it is important to note that calculators may not always provide accurate or exact solutions. It is recommended to double check your answer or use a combination of manual and calculator methods for more complex integrals.

5. What is the final solution to this integral?

The final solution to this integral is (4/3)x^(11/2)-(44/7)x^(9/2)+8x^(5/2)+C, where C is the constant of integration. It is important to always include the constant of integration when solving integrals, as it accounts for all possible solutions that may differ by a constant value.

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