Indefinite Integration Calculus

In summary, by using u-substitution, the integral can be solved to get an answer of 4+2√x-4ln(2+√x) + C or 2√x-4ln(2+√x) + C, as the constant can vary.
  • #1
stoofertje
1
0
1. So I need to solve the following integral


∫1/(2+√x)



The Attempt at a Solution


By double integrating with u-substitution, I got to the following answer: 4+2√x-4ln(2+√x) + C

I can't find out where I go wrong, cause the answer is 2√x-4ln(2+√x), it has been a while, so maybe the +4 just adds to the constant?


Thanks in advance guys,
 
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  • #2
stoofertje said:
1. So I need to solve the following integral


∫1/(2+√x)



The Attempt at a Solution


By double integrating with u-substitution, I got to the following answer: 4+2√x-4ln(2+√x) + C

I can't find out where I go wrong, cause the answer is 2√x-4ln(2+√x), it has been a while, so maybe the +4 just adds to the constant?
Yes, your answer and the official one you showed differ only by a constant, so both are correct.
 

FAQ: Indefinite Integration Calculus

What is indefinite integration calculus?

Indefinite integration calculus is a mathematical concept that involves finding the anti-derivative of a given function. It is used to evaluate the area under a curve and solve various real-world problems in physics, engineering, and economics.

How is indefinite integration different from definite integration?

The main difference between indefinite and definite integration is that indefinite integration results in a general formula, whereas definite integration gives a specific numerical value. Indefinite integration is also known as anti-differentiation, while definite integration is used to find the area under a curve between two points.

What are the basic rules of indefinite integration calculus?

The basic rules of indefinite integration include the power rule, which states that the integral of x^n is equal to (x^(n+1))/(n+1), and the constant multiple rule, which states that the integral of k*f(x) is equal to k times the integral of f(x). Other rules include the sum rule, difference rule, and substitution rule.

How is indefinite integration used in real-life applications?

Indefinite integration is used in various fields such as physics, engineering, and economics to solve real-world problems. For example, it can be used to calculate the distance traveled by an object given its velocity function, or to find the optimal production level for a company to maximize profits.

What are some common techniques for solving indefinite integration problems?

Some common techniques for solving indefinite integration problems include using the basic rules of integration, integration by parts, and integration by substitution. Other techniques include using trigonometric identities and partial fractions to simplify the integral before applying the basic rules.

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