Solve Integral Analytically: Int[(1+x^2)^-n e^-x^2]dx

In summary, an integral is a mathematical concept for finding the area under a curve on a graph. Solving an integral analytically means finding the exact solution using techniques such as substitution, integration by parts, or partial fractions. The function (1+x^2)^-n e^-x^2 is commonly used in statistics and probability to represent the normal distribution. Integration is used to find the area under the curve and determine probabilities. Common techniques for solving integrals analytically include substitution, integration by parts, partial fractions, trigonometric substitutions, and the use of integration tables or software.
  • #1
matt_crouch
161
1
can someone suggest a method to solve an integral of the form analytically?
##\int \left[\frac{1}{(1+x^{2})}\right]^{-n}e^{-x^{2}}dx##
 
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  • #2
Is the bracket a floor function? Otherwise you can use the reciprocal to get (1+x2)n. In that case the infinite integral can be done, but the indefinite integral can be expressed only in terms of the erf.
 

Related to Solve Integral Analytically: Int[(1+x^2)^-n e^-x^2]dx

What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is used to calculate the total value of a function within a given range.

What does it mean to solve an integral analytically?

Solving an integral analytically means finding the exact solution to the integral using mathematical techniques such as substitution, integration by parts, or partial fractions.

What is the function (1+x^2)^-n e^-x^2 used for?

This function is commonly used in statistics and probability to represent the probability density function of the normal distribution with a mean of 0 and standard deviation of 1.

What is the purpose of using integration to solve this function?

Integrating this function allows us to find the area under the curve, which can represent the probability of a specific event occurring in a normal distribution.

What are some common techniques for solving integrals analytically?

Some common techniques include substitution, integration by parts, partial fractions, trigonometric substitutions, and the use of integration tables or software.

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