00:01
So problem 46 says that we have to integrate root x, t raised to the power root x, dx.
00:12
So let's substitute root x as, or in fact we can substitute x as t square, is one and the same.
00:24
So let's substitute x as t square.
00:27
So this implies that dx will be 2t d t.
00:32
So, using this substitution, the integral becomes, this will be root of t square, e -raise to the power root of t square and d x is 2 t d t.
00:46
So this can further be written as 2 comes outside.
00:50
This is t, this is e -raise to the power t, this is t once again and d t.
00:55
So this finally becomes t -square e -r -r -raised to the power t d t.
01:00
This can be integrated using integration by parts.
01:03
So this will be the first term and this will be the second term.
01:05
Term.
01:06
So the first term remains as it is integration of second term will be e raised to the power t minus integration of differentiation of t squared 2t.
01:17
Integration of second term e raised to the power t and once again we have to do integration...