# Trigonomic Integration question

• jordan123
In summary, the integral of ((1+x)/(1+(x^2))) dx can be split into two separate integrals, one being a trigonometric function and the other a logarithmic function. The first integral is straightforward, while the second requires an ordinary substitution.
jordan123

## Homework Statement

Sorry for the lack of latex.

The question is this.

Integral of ((1+x)/(1+(x^2))) dx

If someone could put that together on latex, that would be awesome!

## The Attempt at a Solution

Im not exactly sure what to do, at all. So really any help is great. Even just a hint and I will probably get it. Thanks!

Split into two integrals.
$$\int \frac{1 + x}{1 + x^2}dx$$
$$= \int \frac{1}{1 + x^2} dx + \int \frac{x}{1 + x^2} dx$$

The first is pretty straightforward. The second requires only an ordinary substitution.

((1+x)/(1+(x^2))) dx = (1/(1+(x^2)) dx+(x)/(1+(x^2)) dx

Yes, first part is trigonometric and second is log..

Do you mean

$$\int \frac{1 + x} {1 + x^2} dx$$

Re-write the integrand as two terms

Mark44 said:
Split into two integrals.
$$\int \frac{1 + x}{1 + x^2}dx$$
$$= \int \frac{1}{1 + x^2} dx + \int \frac{x}{1 + x^2} dx$$

The first is pretty straightforward. The second requires only an ordinary substitution.

lol, thanks.

## 1. What is trigonometric integration?

Trigonometric integration is a method used to find the integral of a trigonometric function. It involves using various trigonometric identities and techniques to simplify the function and then integrating it using standard integration rules.

## 2. How do you solve a trigonometric integration question?

To solve a trigonometric integration question, you first need to identify the function and determine which trigonometric identities and techniques can be used to simplify it. Then, use standard integration rules to integrate the function. Finally, evaluate the integral and simplify the solution as much as possible.

## 3. What are some common trigonometric identities used in integration?

Some common trigonometric identities used in integration include the Pythagorean identities, double-angle identities, half-angle identities, and the product-to-sum identities. These identities help to simplify trigonometric functions and make them easier to integrate.

## 4. Can trigonometric integration be used for any type of trigonometric function?

In theory, yes, trigonometric integration can be used for any type of trigonometric function. However, some functions may require more complex techniques or may not have a closed-form solution, making them difficult to integrate. In these cases, numerical methods may be used to approximate the integral.

## 5. Why is trigonometric integration important in science?

Trigonometric integration is important in science because many physical phenomena can be described using trigonometric functions. Integrating these functions allows us to calculate important quantities such as displacement, velocity, and acceleration, which are crucial in fields such as physics, engineering, and astronomy.

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