Integrate JSF 2.1 and Spring 3.2 - spring

Question

I want to use my Spring Beans in my JSF application, letting Spring inject my services/repositories in my JSF Managed Beans.
I found a lot of solutions in the Internet, but the only one that worked was the following lines of code:
ApplicationContext ctx = FacesContextUtils.getWebApplicationContext(FacesContext.getCurrentInstance());
albumRepository = (AlbumRepository) ctx.getBean("albumRepository");
albumRepository is the Spring Bean I'm trying to inject.
The problem is that it's really lame, I don't wanna do this in every class, for every injection. I'd like to use anotations, like "#Inject".
Searching an answer in Google, I found that I should integrate JSF and Spring using the following config in faces-config.xml:
<application>
<el-resolver>
org.springframework.web.jsf.el.SpringBeanFacesELResolver
</el-resolver>
</application>
Then, I should be able to use my Spring Beans with the annotation "#ManagedProperty(value="#{albumRepository}")". I tried it, but I aways get the error "The property albumRepository for the managed bean does not exist".
Searching again in Google I found out that I could use the Spring annotations to do my injections, the only thing i'd need would be to register the package where my managed beans are located in the applicationContext.xml. I've done it, but Spring just ignores my annotations (#Inject and #Autowired, I tried both).
After all these failures I tried to stop using the JSF annotations (#ManagedBean and #ViewScoped), instead, I used Spring ones (#Controller and #Scope). Now JSF doesn't even recognize the beans.
What am I doing wrong?
Edit: My ApplicationContext.xml
<context:annotation-config/>
<jpa:repositories base-package="com.ae.repository" />
<context:component-scan base-package="com.ae.client.web, com.ae.service" />
<!-- Data Source -->
<bean id="dataSource" class="org.springframework.jdbc.datasource.DriverManagerDataSource">
<property name="driverClassName"><value>com.mysql.jdbc.Driver</value></property>
<property name="url"><value>jdbc:mysql://localhost:3306/academia</value></property>
<property name="username"><value>root</value></property>
<property name="password"><value>root</value></property>
</bean>
<bean id="jpaAdapter" class="org.springframework.orm.jpa.vendor.HibernateJpaVendorAdapter">
<property name="database" value="MYSQL" />
<property name="showSql" value="true" />
</bean>
<bean id="entityManagerFactory" class="org.springframework.orm.jpa.LocalContainerEntityManagerFactoryBean">
<property name="dataSource" ref="dataSource" />
<property name="jpaVendorAdapter" ref="jpaAdapter" />
<property name="persistenceXmlLocation" value="/META-INF/persistence-web.xml"/>
</bean>
<bean id="transactionManager" class="org.springframework.orm.jpa.JpaTransactionManager">
<property name="entityManagerFactory" ref="entityManagerFactory" />
</bean>
Edit: My web.xml
<!-- Spring -->
<context-param>
<param-name>contextConfigLocation</param-name>
<param-value>/WEB-INF/applicationContext.xml</param-value>
</context-param>
<listener>
<listener-class>org.springframework.web.context.ContextLoaderListener</listener-class>
</listener>
<listener>
<listener-class>org.springframework.web.context.request.RequestContextListener</listener-class>
</listener>
<!-- JSF -->
<context-param>
<param-name>javax.faces.PROJECT_STAGE</param-name>
<param-value>Development</param-value>
</context-param>
<servlet>
<servlet-name>Faces Servlet</servlet-name>
<servlet-class>javax.faces.webapp.FacesServlet</servlet-class>
<load-on-startup>1</load-on-startup>
</servlet>
<servlet-mapping>
<servlet-name>Faces Servlet</servlet-name>
<url-pattern>/faces/*</url-pattern>
</servlet-mapping>
<session-config>
<session-timeout>
30
</session-timeout>
</session-config>
<context-param>
<param-name>javax.faces.STATE_SAVING_METHOD</param-name>
<param-value>server</param-value>
</context-param>
<welcome-file-list>
<welcome-file>faces/index.xhtml</welcome-file>
</welcome-file-list>
<!-- Primefaces -->
<filter>
<filter-name>PrimeFaces FileUpload Filter</filter-name>
<filter-class>org.primefaces.webapp.filter.FileUploadFilter</filter-class>
</filter>
<filter-mapping>
<filter-name>PrimeFaces FileUpload Filter</filter-name>
<servlet-name>Faces Servlet</servlet-name>
</filter-mapping>

Answer 1

In your web.xml has context param like this ?
<context-param>
<param-name>contextConfigLocation</param-name>
<param-value>classpath:/*Context.xml</param-value>
</context-param>
Also can you send listener about spring in your web.xml

Answer 2

If you want Spring IOC container to manage all your beans. Use one of #Component, #Named or javax.annotation.ManagedBean annotation and you can inject them using #Autowired or #Inject. Don't forget to use Spring's #Scope for any of those.
See Documentation
If you want to use JSF IOC container as well along with Spring IOC container, you can inject Spring beans into a JSF bean using #ManagedProperty.
See Also:
#Scope("request") not working
How does Spring autowire by name when more than one matching bean is found?