# Multiplier for the whole integral

• Muppetmaster
In summary, the conversation discusses an integral containing a constant, pi, outside the integral instead of inside. The integral appears to not have an elementary anti-derivative, and it is suggested that a series expansion may be necessary to find a solution. It is also mentioned that the integral is not found in a textbook and is not easily solvable.
Muppetmaster

## Homework Statement

$\pi[\int \right[ \frac{\sqrt{x^2+1}}{x^4+sin(x)^2}\left]\;dx$

As above

## The Attempt at a Solution

Is there some sort of identity not sure even where to start this one?

Sorry that pi is obviously meant to be a multiplier for the whole integral if that isn't clear.

It's not actually outside per se.

You can easily put it before the dx in a relevant format relation to the equation.

It's just a constant outside the integral instead of inside so think of it as the +C if that helps.

Last edited:

Where did you get this integral from? By observation, it looks like an integral without an elementary anti-derivative.

rock.freak667 said:
Where did you get this integral from? By observation, it looks like an integral without an elementary anti-derivative.

In an advanced textbook, I assume there is a solution but it might as you say be some sort of Taylor series type equation?

I admit it's not technically homework but I thought this would be the place to put it?

wolfram says "No!" :P

Given that you're adding a power of x to a trigonometric function of x in the denominator, I doubt it would be doable. You could of course do a series expansion around some point and integrate each term in the series individually, but I'm not sure if you'd be able to find a closed-form expression for all the series coefficients.

What was the entire statement of the problem? Was it an indefinite integral as you show or a definite integral?

## 1. What is a multiplier for the whole integral?

A multiplier for the whole integral is a constant that is multiplied to an entire integral in order to change its value. This is often used in integration by substitution, where the substitution function is multiplied to the integral to simplify the integration process.

## 2. How do I determine the appropriate multiplier for an integral?

The appropriate multiplier for an integral depends on the substitution function used. It is usually chosen in a way that the derivative of the substitution function cancels out with some part of the integral, making the integration process easier. It may require some trial and error or knowledge of common substitutions to determine the appropriate multiplier.

## 3. Can a multiplier be used for all types of integrals?

Yes, a multiplier can be used for all types of integrals as long as it is appropriate for the specific integral being solved. However, it is most commonly used in integration by substitution.

## 4. How does a multiplier affect the value of the integral?

A multiplier affects the value of the integral by changing it proportionally. For example, if the multiplier is 2, the value of the integral will be twice its original value. However, the overall value of the integral will still be the same as long as the multiplier is applied correctly.

## 5. Can a multiplier be used to solve difficult integrals?

Yes, a multiplier can be a useful tool in solving difficult integrals. It can simplify the integration process and make it easier to solve complex integrals. However, it is important to choose the appropriate multiplier and use it correctly in order to get the correct result.

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