Kotlin Android Extensions with Android library module https://youtrack.jetbrains.com/issue/KT-16934

app_build.gradle

apply plugin: 'com.android.application'
apply plugin: 'kotlin-android'
apply plugin: 'kotlin-android-extensions'

android {
    compileSdkVersion 25
    buildToolsVersion "25.0.2"
    defaultConfig {
        applicationId "com.example.kxt"
        minSdkVersion 15
        targetSdkVersion 25
        versionCode 1
        versionName "1.0"
    }
}

dependencies {
    compile 'com.android.support:appcompat-v7:25.2.0'
    compile "org.jetbrains.kotlin:kotlin-stdlib-jre7:$kotlin_version"
    compile project(':library')
}

app_src_main_java_com_example_kxt_MainActivity.kt

package com.example.kxt

import android.os.Bundle
import android.support.v7.app.AppCompatActivity
import kotlinx.android.synthetic.main.test.*

class MainActivity : AppCompatActivity() {

    override fun onCreate(savedInstanceState: Bundle?) {
        super.onCreate(savedInstanceState)
        setContentView(R.layout.test)
        image_view.scaleType = ImageView.ScaleType.CENTER
    }
}

build.gradle

buildscript {
    ext.kotlin_version = '1.1.0'
    repositories {
        jcenter()
    }
    dependencies {
        classpath 'com.android.tools.build:gradle:2.3.0'
        classpath "org.jetbrains.kotlin:kotlin-gradle-plugin:$kotlin_version"
    }
}

allprojects {
    repositories {
        jcenter()
    }
}

library_build.gradle

apply plugin: 'com.android.library'

android {
    compileSdkVersion 25
    buildToolsVersion "25.0.2"

    defaultConfig {
        minSdkVersion 15
        targetSdkVersion 25
    }
}

library_src_main_res_layout_test.xml

<?xml version="1.0" encoding="utf-8"?>
<FrameLayout xmlns:android="http://schemas.android.com/apk/res/android"
             android:layout_width="match_parent"
             android:layout_height="match_parent">

    <ImageView
        android:id="@+id/image_view"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        />

</FrameLayout>

Still it does not work v. 1.3.72

Yes, this is sample code for the issue reported over 3 years ago. The issue has been closed but the issue is not fixed, the latest issue tracking this can be found here.