... any ideas?itzela said:I'm doing a diff eq problem and I got stuck on the part where I have to integrate
e^(x^2)dx. I tried using substitution but that didn't work
The general approach to integrating e^(x^2)dx is to use a combination of techniques, such as u-substitution and integration by parts, to simplify the integral and solve for the antiderivative. It may also be helpful to use trigonometric or logarithmic identities to simplify the expression.
e^(x^2)dx is a common function that appears in many differential equation problems, especially those involving growth and decay. Its integration can help solve for the general solution of the differential equation and provide insight into the behavior of the system.
One special property of e^(x^2)dx is that it is an even function, meaning that it is symmetric about the y-axis. This can be useful in certain integration techniques, such as integration by parts, as it allows for the cancellation of terms to simplify the integral.
One way to check your work when integrating e^(x^2)dx is to take the derivative of your antiderivative and see if it equals the original integrand. You can also use online integration calculators or graphing software to plot the function and see if it matches your solution.
One tip for solving difficult integrals involving e^(x^2)dx is to try different substitution strategies, such as letting u = x^2 or u = e^(x^2). You can also try manipulating the expression using algebraic techniques, such as completing the square or using trigonometric identities. Additionally, practicing and familiarizing yourself with common integrals involving e^(x^2)dx can help you recognize patterns and approaches to solving them.