Integrate e^(2x)

To integrate e^(2x), integration by substitution can be used.

2x=u, you're left with an intergrand of e^u. 

S: = integral sign

S: e^u dx. In this case we are still integrating the intergrand in terms of x so we much switch it so that we are integrating in terms of u, we do this by differentiating u=2x. this equals du/dx=2. Through simple re-arrangement we get dx= 0.5du. Now we cna sub this into our new integral.

0.5S: e^u du. e to any power, when integrated is just e to that same power so we get 0.5e^u. 

Now all that's left is to sub back in the value of u which then turns our answer to 0.5e^(2x)