sparkle123 said:How do you get that the integral of 4x/(1+4x^2) = 1/2*ln(1_4x^2) ?
I have no clue. I tried u substitution with y=4x^2 but that got me nowhere.
Thanks!
There are several methods to solve integrals, such as substitution, integration by parts, and trigonometric substitution. The most common approach is to look for patterns in the integrand and use the appropriate technique based on those patterns. Practice and familiarity with different methods will also help in identifying the most suitable approach.
Complex integrals can be solved by breaking them down into simpler integrals using techniques like partial fractions or trigonometric identities. In some cases, it may also be necessary to use advanced techniques such as contour integration.
The general steps to solve an integral are: 1) identify the method to use, 2) apply any necessary algebraic manipulation, 3) evaluate the integral using the chosen method, and 4) check the answer for correctness. It is important to be familiar with the different methods and practice regularly to improve problem-solving skills.
Yes, there are several helpful tips and tricks for solving integrals. Some common techniques include using symmetry, choosing appropriate substitutions, and breaking down complex integrals into smaller parts. It is also important to carefully check the limits of integration and any algebraic manipulation done during the solving process.
A calculator can be used to solve integrals when the integral is a simple one or when the calculator has the appropriate integration function. However, it is important to note that relying solely on a calculator may hinder understanding of the underlying concepts and limit problem-solving skills. It is recommended to use a calculator only as a tool to check answers and not as the primary method of solving integrals.