# Substituting for Intergral: Tricky Intergral

• Lee
In summary, a tricky integral is one that cannot be solved using basic integration techniques. Substituting for an integral is necessary to simplify the integrand and make it more manageable. Some common substitution methods for tricky integrals include u-substitution, trigonometric substitution, and hyperbolic substitution. The choice of substitution method depends on the form of the integrand. Some tips for solving tricky integrals include careful analysis of the integrand, trying different substitution methods, and regular practice.
Lee
Which substituation would I need to use for this intergral;

[y.du/(y^2 + (x - u)^2)]

The integrand looks like $$1/(1+x^2)$$ which has antiderivative arctan(x). Try to make substitutions to match that expression.

Got it, take the y out the intergral, make b=x-u then db=-du sub in and use the arctan intergral, getting -tan^-1((x-u)/y)

## 1. What is a tricky integral?

A tricky integral is an integral that cannot be solved using basic integration techniques such as substitution, integration by parts, or partial fractions. These integrals often involve complex functions or expressions that require advanced mathematical techniques to solve.

## 2. Why is substituting for an integral necessary?

Substituting for an integral allows us to simplify the integrand and make it easier to integrate. It also helps us to find a new variable that makes the integral more manageable, especially for tricky integrals.

## 3. What are some common substitution methods for tricky integrals?

Some common substitution methods for tricky integrals include u-substitution, trigonometric substitution, and hyperbolic substitution. These methods involve replacing the variable in the integral with a new variable to simplify the integrand.

## 4. How do I know when to use a specific substitution method?

The choice of substitution method depends on the form of the integrand. For example, if the integrand contains a square root, we can use u-substitution. If it contains expressions involving trigonometric functions, we can use trigonometric substitution. It is important to carefully analyze the integrand before choosing a substitution method.

## 5. Are there any tips for solving tricky integrals?

Yes, some tips for solving tricky integrals include, carefully analyzing the integrand, trying different substitution methods, and practicing regularly. It is also helpful to review basic integration techniques and to become familiar with the properties of different functions and their derivatives.

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