# Integral of -: (v^2+2v-1)/(v^3+v^2+v+1)

• amaresh92
In summary, the purpose of finding the integral of an expression is to determine the area under the curve of the function represented by the expression. It is a fundamental concept in calculus and has various real-life applications in fields such as physics, engineering, and economics. It is not possible to find the integral without using calculus, and to solve it, techniques such as integration by parts, substitution, or partial fractions can be used. The steps involved in solving the integral depend on the technique used and can involve simplifying the expression and using basic integration rules. Some real-life applications of finding the integral include calculating work, velocity, and profit, as well as in engineering and economics for calculations such as stress-strain curves and marginal cost and revenue.
amaresh92
how to find the integral of -: (v^2+2v-1)/(v^3+v^2+v+1)

Partial fractions decomposition.

Note that the denominator is divisible by (v+1):
$$(v^{3}+v^{2}+v+1)/(v+1)=v^{2}+1$$

Notice that $$v^3+v^2+v+1=(v+1)(v^2+1)$$. Use the method of partial fractions, once it's done it's very easy.

losiu99 said:
Notice that $$v^3+v^2+v+1=(v+1)(v^2+1)$$. Use the method of partial fractions, once it's done it's very easy.
HA! I beat you to it!
We oldies are still the best!

Yeah, soo true Maybe next time...

## 1. What is the purpose of finding the integral of this expression?

The integral of an expression is used to determine the area under the curve of the function represented by the expression. It is a fundamental concept in calculus and is used in various fields such as physics, engineering, and economics.

## 2. Is it possible to find the integral of this expression without using calculus?

No, it is not possible to find the integral of this expression without using calculus. Integration is a concept in calculus that involves finding the anti-derivative of a function. Without using calculus, it is not possible to find the anti-derivative of a function.

## 3. How do you solve this integral?

To solve this integral, you can use techniques such as integration by parts, substitution, or partial fractions. It is a complex integral and may require multiple steps to solve.

## 4. Can you explain the steps involved in solving this integral?

The steps involved in solving this integral depend on the technique used. Generally, the first step is to simplify the expression by factoring out common terms. Then, you can use techniques like substitution or integration by parts to transform the integral into a simpler form. Finally, you can use basic integration rules or tables to solve the integral.

## 5. What are some real-life applications of finding the integral of this expression?

Finding the integral of this expression can be applied in various real-life scenarios such as calculating the work done by a force, determining the velocity of an object, or finding the total profit of a business. It is also used in fields like engineering to calculate the area under a stress-strain curve, and in economics to determine the marginal cost and revenue of a product.

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