Let's have a look at
our second integral.
You can see here that this looks like
a function of a function equation.
So let's see how we deal with this.
Remember, we've done a very similar
example in the previous lecture.
So let's attempt
to integrate this.
It's still an indefinite integral,
so there are no limits.
That means we will put a plus C at the
end and it's to the power of three dx.
So remember what we said.
If you're integrating something like this,
we're trying to do the exact opposite of
the chain rule when we differentiate.
So, this is the outside function,
this is the inside function.
To start off, we're going to
integrate the outside function
anything on the inside.
So to integrate, you add one to
the power, divide by new power.
And then rather than multiplying
with the differential of the inside,
the differential of the
inside in this case is 10.
We are going to divide it by the
differential of the inside,
and obviously those two values
at the bottom multiply.
So we are adding one to the
power, dividing by new power,
dividing by the
differential of the inside.
Put plus C there or later.
So we've got 10x minus
5 to the power of 4
all over 40 plus C.
And that's your integral.