- #1
Argiris
- 3
- 0
Homework Statement
hey could you help me to calculate the indefinite integral of y=√(x+1)/√(x+2)
Homework Equations
The Attempt at a Solution
tried to set x+1=u and integrate it by substitution but didnt work
Last edited:
Argiris said:Homework Statement
hey could you help me to calculate the indefinite integral of y=√x+1/x+2
Homework Equations
The Attempt at a Solution
tried to set x+1=u and integrate it by substitution but didnt work
Ray Vickson said:It is not clear what your function y is. It could be [tex] y = \sqrt{x} + \frac{1}{x} + 2, [/tex] or [tex] y = \sqrt{\displaystyle x + \frac{1}{x}} + 2, [/tex] or
[tex] y = \sqrt{\displaystyle x + \frac{1}{x} + 2}. [/tex] If you don't want to use LaTeX, you need to use brackets, so the first way I wrote above would be y = (√x) + (1/x) + 2, the second way would be y = √[x + (1/x)] + 2, and the thire way would be y = √[x + (1/x) + 2]. If I read your function using *standard* rules and priorities, it means the first way above.
RGV
micromass said:Try to set [itex]u^2=x+1[/itex]
I don't get that u^3.Argiris said:well i tried it and this transformed the integral into ...
Similar, but slightly different than what micromass suggested.Argiris said:Homework Statement
hey could you help me to calculate the indefinite integral of y=√(x+1)/√(x+2)
Homework Equations
The Attempt at a Solution
tried to set x+1=u and integrate it by substitution but didn't work
http://www.wolframalpha.com/input/?i=int+2+sqrt%28u^2-1%29SammyS said:Use the substitution: [itex]u=\sqrt{x+2}\,,[/itex]
An indefinite integral is a mathematical concept that represents the antiderivative of a function. It is a fundamental concept in calculus, and is used to find the original function when given its derivative.
The process for calculating an indefinite integral involves using integration techniques, such as substitution, integration by parts, or trigonometric substitution, to find the antiderivative of a given function. This process requires knowledge of basic integration rules and formulas.
A definite integral has a specific interval of integration, while an indefinite integral does not. This means that a definite integral will give a specific numerical value, while an indefinite integral will give a function as the solution.
Choosing the appropriate integration technique depends on the form of the function. The best way to decide which technique to use is to practice and gain familiarity with each method. In general, it is helpful to look for patterns and use your knowledge of basic integration rules to determine the best technique for a given function.
Indefinite integrals are important because they allow us to find the original function when given its derivative. This is useful in many areas of science and engineering, as well as in other branches of mathematics. It also provides a way to find the area under a curve, which has many practical applications.