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. 1. 2. 3. 4.

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: