访问不到主页index.jsp的原因是servlet-api.jar包有冲突，删除lib的servlet-api.jar，如果报错则添加Apache Tomcat下的 servlet-api.jar 即可。

HTTP Status 500 - Unable to compile class for JSP:

type Exception report

message Unable to compile class for JSP:

description The server encountered an internal error that prevented it from fulfilling this request.

exception

org.apache.jasper.JasperException: Unable to compile class for JSP:

An error occurred at line: [43] in the generated java file: [D:\tomcat8.0\apache-tomcat-8.0.14\work\Catalina\localhost\test_project\org\apache\jsp\index_jsp.java]

The method getDispatcherType() is undefined for the type HttpServletRequest

Stacktrace:

org.apache.jasper.compiler.DefaultErrorHandler.javacError(DefaultErrorHandler.java:103)

org.apache.jasper.compiler.ErrorDispatcher.javacError(ErrorDispatcher.java:199)

org.apache.jasper.compiler.JDTCompiler.generateClass(JDTCompiler.java:450)

org.apache.jasper.compiler.Compiler.compile(Compiler.java:361)

org.apache.jasper.compiler.Compiler.compile(Compiler.java:336)

org.apache.jasper.compiler.Compiler.compile(Compiler.java:323)

org.apache.jasper.JspCompilationContext.compile(JspCompilationContext.java:564)

org.apache.jasper.servlet.JspServletWrapper.service(JspServletWrapper.java:357)

org.apache.jasper.servlet.JspServlet.serviceJspFile(JspServlet.java:396)

org.apache.jasper.servlet.JspServlet.service(JspServlet.java:340)

javax.servlet.http.HttpServlet.service(HttpServlet.java:725)

org.apache.tomcat.websocket.server.WsFilter.doFilter(WsFilter.java:52)

note The full stack trace of the root cause is available in the Apache Tomcat/8.0.14 logs.

Apache Tomcat/8.0.14