How do I integrate 2^x?

Let's first consider the differential of 2^x. We know that this becomes ln(2)*2^x. We can compare this to the integrand and see that this is very close indeed! The only problem is that ln(2). So now consider 2^x / ln(2). When we differentiate this we get 2^x. So we conclude that the integral of 2^x is 2^x / ln(2) + C (don't for get the +C!). This is sometimes known as the reverse chain rule.