- #1
revlvr357
- 4
- 0
hey guys, the function is...
(x dx) / (x^2 + 5x + 6)
please integrate it. please.
thanks so much,
Matt
(x dx) / (x^2 + 5x + 6)
please integrate it. please.
thanks so much,
Matt
Mathematica said:In[1]= Integrate[x/(x^2 + 5x + 6), x]
Out[1]= -2 Log[2 + x] + 3 Log[3 + x]
berkeman said:Here's a hint -- cheat and plug the integral into Mathematica, and then look at the answer and differentiate it to see how it can become the integrand. Then think about what you would have to do with the integrand to get it into the original form of the question...
Integrating a function is the process of finding the area under a curve or the accumulation of a quantity over an interval of values. It is commonly used in mathematics, physics, and engineering to solve problems involving rates of change or accumulation.
To integrate a function, you can use various techniques such as substitution, integration by parts, or partial fractions. The most commonly used method is the Fundamental Theorem of Calculus, which states that the integral of a function is equal to the area under its curve.
Differentiation and integration are inverse operations of each other. Differentiation is the process of finding the rate of change of a function, while integration is the process of finding the accumulation of a quantity over an interval. In other words, differentiation is finding the slope of a curve, while integration is finding the area under the curve.
Integrating a function has various applications in real life, such as calculating the net displacement of an object from its velocity function, determining the total cost of a product from its rate of change, or finding the total amount of energy used over a period of time.
No, not all functions can be integrated. Some functions have indefinite integrals, meaning they can be integrated to give an output, while others have no definite integral, making it impossible to integrate them. These types of functions are called non-integrable functions.