Math $1510$

Written Assignment $4$

$4\mathrm{.}7-4\mathrm{.}9,5\mathrm{.}1-5\mathrm{.}5$

$9.$ Substitution. Consider the integral

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}sin{h}^3(x)cos{h}^3(x)dx$

a$)$ Evaluate the integral by making the substitution $u=sinh(x).$

b$)$ Evaluate the integral by making the substitution $u=cosh(x).$

c$)$ Use the identity $sinh(2x)=2sinh(x)cosh(x)$ to rewrite the integrand and then evaluate the integral by making the substitution $u=2x.$