Integral of exp(x)*sqrt(5-cos(x)) | Hard

Thread starter relativitydude
Start date Oct 31, 2004
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Hard Integral

In summary, the formula for finding the integral of exp(x)*sqrt(5-cos(x)) is ∫exp(x)*sqrt(5-cos(x)) dx = √(2π)*(1+2*e^(5/2))*erf(x/√2) + C, and it can be solved by hand using techniques such as substitution or integration by parts. The integral has various applications in physics, engineering, and other fields and can be used to calculate area, volume, and work done. There is no specific shortcut to finding the integral, but techniques such as integration by parts can help simplify it. It is also helpful to have knowledge of basic integration rules and properties.

Oct 31, 2004

relativitydude

Integral of exp(x)*sqrt( 5 - cos(x))

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Nov 1, 2004

Tide

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Homework Helper

Is that a cosine or a hyperbolic cosine?

Nov 1, 2004

logicalman

Maybe you should try:

[tex] 5-cosx = x^2 [/tex]

then take "log" on both sides and proceed from there. :tongue:

Nov 1, 2004

spacetime

Try integrating by parts.

1. What is the formula for finding the integral of exp(x)*sqrt(5-cos(x))?

The formula for finding the integral of exp(x)*sqrt(5-cos(x)) is ∫exp(x)*sqrt(5-cos(x)) dx = √(2π)*(1+2*e^(5/2))*erf(x/√2) + C, where erf(x) is the error function and C is the constant of integration.

2. How do you solve the integral of exp(x)*sqrt(5-cos(x))?

To solve the integral of exp(x)*sqrt(5-cos(x)), you can use techniques such as substitution or integration by parts. It is also helpful to use mathematical software or tables to find the antiderivative.

3. What are the applications of the integral of exp(x)*sqrt(5-cos(x))?

The integral of exp(x)*sqrt(5-cos(x)) has various applications in physics, engineering, and other fields. It can be used to calculate the area under a curve, the volume of a solid of revolution, and the work done by a variable force. It also has applications in probability and statistics.

4. Can the integral of exp(x)*sqrt(5-cos(x)) be solved by hand?

Yes, the integral of exp(x)*sqrt(5-cos(x)) can be solved by hand using techniques such as substitution or integration by parts. However, it may be more efficient to use mathematical software or tables to find the antiderivative.

5. Is there a shortcut to finding the integral of exp(x)*sqrt(5-cos(x))?

There is no specific shortcut for finding the integral of exp(x)*sqrt(5-cos(x)), but there are techniques such as integration by parts that can help simplify the integral. It is also helpful to have knowledge of basic integration rules and properties to solve the integral efficiently.