00:01
So we have integral from 0 to 1, x squared times 2 to the x dx.
00:11
So i will take u as x squared and dv as 2 to the x.
00:18
So du is 2x, v is 2 to the x over ln2.
00:26
All right, so integral of udv is equal to uv minus integral of v.
00:34
D u so that's equal to x squared times 2 to the x over ln of 2 minus v du so that's 2 to the x over ln 2 times 2x so factoring out 2 over ln 2 so we'll get x squared times 2 to the x over ln 2 minus 2 over ln 2 times integral of x times 2 to the x.
01:13
All right, so now we need to integrate by parts again.
01:18
So let's take x as u.
01:20
So this time u is x, and dv is 2 to the x, d x.
01:27
2 to the x here.
01:29
D u is 1 .v is 2 to the x over ln2.
01:35
So now let's expand that.
01:37
So we will get, again, let's write everything out.
01:41
X squared 2 to the x over ln 2 minus 2 over ln of 2 into uv so x times 2 to the x over ln 2 minus integral of vd u.
02:09
So that's 2 to the x over ln 2 i'm just going to put ln of 2 outside so my minus 1 over ln2 integral of 2 to the x...