How to window.scrollTo() with a smooth effect

I can scroll to 200px using the following

btn.addEventListener("click", function(){
    window.scrollTo(0,200);
})

But I want a smooth scroll effect. How do I do this?

2018 Update

Now you can use just window.scrollTo({ top: 0, behavior: 'smooth' }) to get the page scrolled with a smooth effect.

const btn = document.getElementById('elem');

btn.addEventListener('click', () => window.scrollTo({
  top: 400,
  behavior: 'smooth',
}));

#x {
  height: 1000px;
  background: lightblue;
}

<div id='x'>
  <button id='elem'>Click to scroll</button>
</div>

Older solutions

You can do something like this:

var btn = document.getElementById('x');

btn.addEventListener("click", function() {
  var i = 10;
  var int = setInterval(function() {
    window.scrollTo(0, i);
    i += 10;
    if (i >= 200) clearInterval(int);
  }, 20);
})

body {
  background: #3a2613;
  height: 600px;
}

<button id='x'>click</button>

ES6 recursive approach:

const btn = document.getElementById('elem');

const smoothScroll = (h) => {
  let i = h || 0;
  if (i < 200) {
    setTimeout(() => {
      window.scrollTo(0, i);
      smoothScroll(i + 10);
    }, 10);
  }
}

btn.addEventListener('click', () => smoothScroll());

body {
  background: #9a6432;
  height: 600px;
}

<button id='elem'>click</button>

$('html, body').animate({scrollTop:1200},'50');

You can do this!