- #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##
##\int \left[\frac{1}{(1+x^{2})}\right]^{-n}e^{-x^{2}}dx##
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.
Solving an integral analytically means finding the exact solution to the integral using mathematical techniques such as substitution, integration by parts, or partial fractions.
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.
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.
Some common techniques include substitution, integration by parts, partial fractions, trigonometric substitutions, and the use of integration tables or software.