trot said:Please intergrate: (x+3)/(x^2+4x) is it even possible to integrate this?
The question in the book was (x+2)/(x^2+4x) and it can nicely be integrated to 0.5ln(x^2+4x), but by changing the 2 to a 3 f'(x) don't go into each other. if you know what i mean.
DonAntonio said:First:
$$\frac{1}{x^2+4x}=\frac{1}{4}\left[\frac{1}{x}-\frac{1}{x+4}\right]$$,
so that
$$\int\frac{x+3}{x^2+4x}=\frac{1}{2}\int\frac{2x+4}{x^2+4x}dx+\int\frac{1}{x^2+4x}dx=\frac{1}{2}\log(x^2+4x)+\frac{1}{4}\log\left(\frac{x}{x+4}\right)+C$$
Ray Vickson said:You are not supposed to do a student's homework---just give hints.
RGV
Integrating a function means finding the area under the curve of that function. This can be done using various techniques such as substitution, integration by parts, or using numerical methods. However, not all functions can be integrated, and even if they can, the process may be very complex and time-consuming.
It is possible to integrate many different types of functions, including polynomial, trigonometric, exponential, and logarithmic functions. However, there are also functions that cannot be integrated using standard techniques. In such cases, numerical methods can be used to approximate the integral.
There is no simple answer to this question. Some functions have well-known integrals that can be easily found using basic integration rules. However, there is no general method to determine if a function can be integrated. It often requires knowledge of various integration techniques and practice in solving integrals.
Yes, there are many software programs and online tools available that can help with integration. These tools use numerical methods to approximate the integral. However, it is important to remember that these methods may not always give exact solutions and may introduce some errors.
The best way to improve your integration skills is through practice. Start with simpler functions and use basic integration techniques. As you become more comfortable, move on to more complex functions and learn new integration techniques. It is also helpful to review the fundamental concepts of calculus and familiarize yourself with the rules and properties of integration.