# Integration with Inverse Trig: Simplifying with Substitution

• crm08
In summary, integration with inverse trigonometric functions is a technique used to solve integrals involving inverse trigonometric functions such as arcsine, arccosine, and arctangent. The most commonly used inverse trigonometric functions in integration are arcsine, arccosine, and arctangent. To integrate with these functions, you can use integration by substitution, where you substitute the inverse trigonometric function with a variable and use trigonometric identities to solve the integral. Some tips for solving these types of integrals include identifying the appropriate substitution, using trigonometric identities, and being familiar with the derivatives of inverse trigonometric functions. The applications of integration with inverse trigonometric functions include solving problems in physics
crm08

## Homework Statement

$$\int\frac{dx}{9x^{2}+1}$$

## Homework Equations

$$\frac{d}{dx}(arctan(x))$$ = $$\frac{1}{1+x^{2}}$$

## The Attempt at a Solution

The other problems in this homework set all use the substitution rule but I can't find anything that would simplify the problem, my other guess would be to pull a (1/9) out, but then that would result in having a denominator = (x^2 + (1/9)), could someone get me on the right track, I have a feeling that I'm overlooking something obvious

Try u = 3x

## 1. What is integration with inverse trig?

Integration with inverse trigonometric functions is a technique used to solve integrals involving inverse trigonometric functions such as arcsine, arccosine, and arctangent.

## 2. What are the common inverse trigonometric functions used in integration?

The most commonly used inverse trigonometric functions in integration are arcsine (sin-1), arccosine (cos-1), and arctangent (tan-1).

## 3. How do you integrate with inverse trigonometric functions?

To integrate with inverse trigonometric functions, you can use integration by substitution, where you substitute the inverse trigonometric function with a variable and then use the appropriate trigonometric identities to solve the integral.

## 4. What are some tips for solving integrals involving inverse trigonometric functions?

Some tips for solving integrals involving inverse trigonometric functions include identifying the appropriate substitution, using trigonometric identities to simplify the integral, and being familiar with the derivatives of inverse trigonometric functions.

## 5. What are the applications of integration with inverse trigonometric functions?

Integration with inverse trigonometric functions is commonly used in physics, engineering, and other fields to solve problems involving angles and circular motion. It is also useful in solving integrals that arise in calculus and other areas of mathematics.

• Calculus and Beyond Homework Help
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
4
Views
400
• Calculus and Beyond Homework Help
Replies
2
Views
344
• Calculus and Beyond Homework Help
Replies
12
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
453
• Calculus and Beyond Homework Help
Replies
22
Views
1K
• Calculus and Beyond Homework Help
Replies
5
Views
579
• Calculus and Beyond Homework Help
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
8
Views
835