00:01
Hello everyone, in this problem we need to evaluate the given integral.
00:05
In the first part we are given with the integral.
00:08
Integral of 2 of x cube minus x power 4 divided by 5 x power 4 minus 4 x power 5 the whole power 4 of dx.
00:23
Now let us take this integral to be i.
00:25
Now let us take substitution t to be 5 x power 4 minus 4 x power 5.
00:34
So now differentiating on both sides it would be dt to be equal to 20 x cube minus 20 x power 4 of dx.
00:47
So from this we get the value of x cube minus x power 4 of dx to be equal to dt by 20.
00:58
So now substituting all these in the i so i will become 2 divided by 20 of integral of 1 divided by t power 4 dt.
01:10
So simplifying this it would be 1 by 10 and rewriting this it can be written as integral of t power minus 4 dt.
01:18
So now integrating this we have this to be 1 by 10 of t power minus 3 divided by minus 3 plus c where c is the constant of integration.
01:31
So now simplifying this it would become minus 1 divided by 30 of 1 by t cube plus c.
01:41
Now substituting the value of t here so it would be minus 1 by 30 of 1 divided by 5 x power 4 minus 4 x power 5 the whole cube plus c...