Which trig sub is needed for this integral?

Thread starter crybllrd
Start date Mar 1, 2012
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Trig

In summary, a trigonometric substitution is a mathematical technique for solving integrals involving trigonometric functions by replacing the variables with trigonometric expressions. It is commonly used for integrals with square roots or rational expressions involving trigonometric functions, and the choice of substitution depends on the form of the integral. However, not all integrals can be solved using this method and it is important to carefully select the correct substitution and simplify the integral using trigonometric identities. It is also recommended to check the answer by differentiating it back to the original integral.

Mar 1, 2012

crybllrd

Homework Statement

[itex]\int\frac{dx}{x(x^{2}-1)^{3/2}}[/itex]

Homework Equations

The Attempt at a Solution

I know I need to use trig sub, but which form? I can't seem to find any that fit this form.

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Mar 1, 2012

LCKurtz

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A triangle with x on the hypotenuse and 1 on a leg suggests ##x=\sec\theta##.

Related to Which trig sub is needed for this integral?

1. What is a trigonometric substitution?

A trigonometric substitution is a mathematical technique used to solve integrals involving trigonometric functions by replacing the variables with trigonometric expressions.

2. When should I use a trigonometric substitution?

Trigonometric substitutions are commonly used when solving integrals with square roots or rational expressions involving trigonometric functions.

3. How do I know which trigonometric substitution to use?

The choice of trigonometric substitution depends on the form of the integral. Generally, you should try to identify which trigonometric identity can be used to simplify the integral.

4. Can I use a trigonometric substitution to solve any integral?

No, not every integral can be solved using a trigonometric substitution. It is a useful technique for specific types of integrals, but there are other methods that may be more appropriate for different types of integrals.

5. Are there any tips for using trigonometric substitutions?

One tip is to always check your answers by differentiating them back to the original integral. Also, make sure to carefully choose the correct trigonometric substitution and use trigonometric identities to simplify the integral as much as possible before evaluating it.