# Need Help with Integral question

• radtad
In summary, the conversation is discussing how to evaluate the integral \int\frac{1}{x^2-6x+8}dx, with one person suggesting using the standard "arctan" method and the other suggesting using partial fractions. They also mention using the substitution x-3=u to simplify the integral, which leads to the "arctanh" function.
radtad
How do you evaluate this integral:

integral(1/(x^2-6x+8)

i don't kno how to subsitute on this or anything. I am completely stuck

It's standard "arctan" type.To see it,try to write the denominator as a sum of squares...

Daniel.

Standard Arctan? I did this on Mathematica's online integral calculator and got the difference of two logarithms. I would do this integral by partial fractions.

$$\int\frac{1}{x^2-6x+8}dx = \int\frac{A}{x-4} + \frac{B}{x-2}dx$$

Sorry.

$$\int \frac{dx}{(x-3)^{2}-1}$$

and then the substituion $x-3=u$

which would give

$$\int \frac{du}{u^{2}-1}$$

which is typically "arctanh"...

Daniel.

## What is an integral?

An integral is a mathematical concept that represents the area under a curve. It is used to calculate the total value of a continuous function within a given interval.

## Why do we need to use integrals?

Integrals are useful in many areas of science, particularly in physics and engineering. They allow us to calculate important values such as total distance traveled, total force applied, and total energy used.

## What is the difference between definite and indefinite integrals?

A definite integral has specific upper and lower limits, and gives a numerical value as the answer. An indefinite integral has no limits and gives a function as the answer.

## How do I solve an integral?

The process for solving an integral depends on the type of integral and the function being integrated. Some methods include substitution, integration by parts, and using special rules such as the power rule or trigonometric identities.

## What is the fundamental theorem of calculus?

The fundamental theorem of calculus states that differentiation and integration are inverse operations. In other words, the derivative of an integral is equal to the original function, and the integral of a derivative is equal to the original function plus a constant.

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