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**Section 6.2: Integration by Substitution**

Objectives: Students will be able to… Use substitution in indefinite integrals Use substitution in definite integrals Solve separable differential equations

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**Find the indefinite integral**

What if we had to find ?

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**Find indefinite integral**

NOTICE ANYTHING??????

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**If you have You can use the substitution method:**

Choose a substitution : u = g(x) Compute du = g’(x)dx Rewrite the integral in terms of the variable u. Replace u by g(x) to obtain an antiderivative in terms of x Check your answer by differentiating Integrating by substitution is to integration, as the chain rule is to differentiation

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**Let’s revisit the last problem…**

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**Examples: Find the indefinite integral.**

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**Sometimes you need to solve for dx:**

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**Find the indefinite integral**

1) 2) 3)

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**What about u? Having difficulty deciding what u should be?**

Check to see if you have one of the following cases. The quantity under a root or raised to a power The quantity in the denominator The exponent on e *Remember some integrands may need to be rearranged to fit one of these

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**Find the indefinite integral:**

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