HOMEWORK $1$

Evaluate the following integrals. SHOW COMPLETE SOLUTIONS. $(10$ points each$)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{x^3+2x^2+9x}$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{(5x-4)dx}{x^4+2x^3}$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{e^{2x}dx}{\sqrt[\phantom{2}]{e^x-1}}($Use Algebraic Substitution$)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{\sqrt[\phantom{2}]{9-4x^2}dx}{x^2}($Use Trigonometric Substitution$)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{4+5cosx}$