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yfatehi
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I need some help evaluating the following integral from 0 to inifinity and a,p,c are positive reals, p>=1
\int\limit_0^\infty\ x^{p-1}e^{-x}e^{-c x^a} dx
\int\limit_0^\infty\ x^{p-1}e^{-x}e^{-c x^a} dx
An integral involving power, exp, and exp(power) is a mathematical expression that involves the integration of a function with variables raised to a power, exponentials, and the exponential of a power. It is used to calculate the area under a curve that is described by these types of functions.
To solve an integral involving power, exp, and exp(power), you can use integration techniques such as substitution, integration by parts, or partial fractions. It is important to first simplify the expression and then apply the appropriate integration technique.
Integrals involving power, exp, and exp(power) have various applications in physics, engineering, and economics. They are used to calculate quantities such as work, energy, and probability in these fields.
Yes, there are special cases of integrals involving power, exp, and exp(power) such as the Gaussian integral and the Fresnel integral. These integrals have specific formulas and techniques for solving them.
Integrals involving power, exp, and exp(power) are used to calculate the area under a curve that is described by these types of functions. This is because integration is essentially a process of finding the area under a curve. It is a fundamental concept in calculus and has many practical applications.