Find Find Find Find Find Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS Rational function: Example Example Find Find Example Find Example Example Find Find

Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS 1 Use long division 2 Check if we can use subsitution 3 Factor q(x) as linear factors or irreducible quadratic Express p(x)/q(x) as a sum of partial fraction 4 q(x)= product of linear factor q(x)= product of quadratic (irred) All distinct Some repeated repeated All distinct case1 case2 case3 case4

Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS q(x)= product of linear factor Example Find All distinct Some repeated case1 case2 Example Find

Find Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS q(x)= product of linear factor All distinct Some repeated case1 case2 Example Example Find

Find Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS q(x)= product of quadratic (irred) repeated All distinct case3 case4 Example Example Find

Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS q(x)= product of quadratic (irred) repeated All distinct case3 case4 Example Example Express only Example Find

rational function of sin and cos Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS rational function of sin and cos 1 Use the following to convert it into rational function 2 Evaluate the integral then use:

Find Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS RATIONALIZING SUBSTITUTIONS Some nonrational functions can be changed into rational functions Example Find

Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

Sec 7.4: INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS