Your Name: $$ Group Project $($Method of Integrations$)$

Math$141-$Cal II

Your Group members' Names: $q,$

No$.1[12$ pts$]$ Write out the form of the partial decomposition of the function. Do not determine the numerical values of the coefficients. Remember to perform long divsion if rational function is improper.

$($a$)\frac{4}{x^2(x-1{)}^3(x^{2}5)}$

$($b$)\frac{x^6}{x^2-4}$

No$.2[10$ pts$]$ Evaluate the integral using trigonometric substitution method. No credits for any other method. Sketch and label the associated right triangle for full credits.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{(x^{2}1{)}^2}$

No$.3[10$ pts$]$ Evaluate the integral using Partial Fraction Method. No credits for any other method.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{9x^2-1}{(x-3)(x^{2}1)}dx$

No$.4[10$ pts$]$ Evaluate the integral using method of integration by parts. No credits for any other method. You may use ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}secd=ln|sectan|C,$ if needed.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}se{c}^3()d$