How do you find the integral of #e^(x^2)#? - Socratic
Apr 27, 2015 · Use some kind of approximation method. There is no nice, finitely expressible antiderivative. (Other that to write: int e^(x^2) dx, of course.)
How do you integrate #int x^2 e^(-x)dx# using integration by
Apr 11, 2018 · How do you integrate #int x^2 e^(-x)dx# using integration by parts? Calculus Techniques of Integration Integration by Parts. 1 Answer
How can I correctly solve the integral of (x^2)/((x^2+1)^2) step by …
Dec 25, 2009 · To solve the integral of (x^2)/((x^2+1)^2), you can use the substitution method by letting u = x^2 + 1. This will result in the integral becoming 1/(2u^2) du, which can then be solved using the power rule.
How do you integrate int (x^2)/(1-x^3) dx? - Socratic
Jun 8, 2015 · You can do a u-substitution. Notice how this can be written as: int x^2*(1/(1-x^3))dx d/(dx)[-x^3] = -3x^2dx, so d/(dx)[(-1/3)*(-x^3)] = x^2dx.
How do you integrate #(x/(x+2))#? - Socratic
May 29, 2016 · We can simplify this way is written: #intx/(x+2)dx=int(x+2-2)/(x+2)dx=int((x+2)/(x+2)-2/(x+2)dx)# #int(1-2/(x+2))dx=int1dx-2int1/(x+2)dx#
How do you integrate #x^2/(x^2+1)#? - Socratic
Jun 28, 2016 · x - arctan x + C x^2/(x^2+1) = (x^2+1 - 1)/(x^2+1) = 1 - ( 1)/(x^2+1) int \ 1 - ( 1)/(x^2+1) \ dx = x - color(red)(int \ ( 1)/(x^2+1) \ dx ) in terms of the red bit, use sub x = tan t, dx = sec^2 t \ dt this makes it \int \ ( 1)/(tan^2 t+1) \ sec^2 t \ dt = \int \ ( 1)/(sec^2 t) \ sec^2 t \ dt = \int \ dt = arctan x - C So the full integral is x - arctan x + C
How do you integrate #int x^2 e^(x^2 ) dx # using ... - Socratic
Apr 30, 2016 · See the explanation section below. To integrate x to a power times e to a power, we expect to differentiate the x and integrate the e to a power int x^2 e^(x^2 ) dx In order to integrate e^(x^2) dx we need an x so that we can use substitution. int x^2 e^(x^2) dx = int x e^(x^2)x dx . Let u = x and dv = e^(x^2)x dx The du = 1 dx and v = 1/2 e^(x^2) int x^2 e^(x^2) …
How do we integrate x^2/(e^x - 1) from xg to infinity? - Physics …
Nov 20, 2018 · The integral of x^2/(e^x - 1) from xg to infinity is a challenging problem that involves the use of advanced mathematical techniques such as integration by parts and the Gamma function. It is not a straightforward integration and requires a thorough understanding of calculus and special functions.
Integral of x^2/(x+2) Solution | Evaluate the Integral - Physics …
Aug 23, 2011 · The domain of the integral of x^2/(x+2) is all real numbers except for x = -2, and the range is all real numbers. 5. How can the integral of x^2/(x+2) be applied in real life? The integral of x^2/(x+2) can be applied in various fields such as engineering, physics, and economics to solve problems involving rates of change, optimization, and area ...
The integration of e^(x^2) - Physics Forums
Dec 11, 2005 · The integration of e^(x^2) is the process of finding the antiderivative of the function e^(x^2). It involves finding a function whose derivative is equal to e^(x^2). Why is the integration of e^(x^2) important? The integration of e^(x^2) is important in many areas of mathematics and science, including probability, statistics, and physics.