 # Section 6.2: Integration by Substitution

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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

Find the indefinite integral
What if we had to find ?

Find indefinite integral
NOTICE ANYTHING??????

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 

Let’s revisit the last problem…

Examples: Find the indefinite integral.

Sometimes you need to solve for dx:

Find the indefinite integral
1) 2) 3)

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

Find the indefinite integral: