5-5-43 usub
X
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CC
When doing this problem, we're going to let U equal X -, 9, so
DU is just DX.
So then when we take the integral, if we have plain old X
in the top, we could solve the top for X here and see that X is
really the same thing as U + 9.
So we're going to have U + 9 / sqrt U DU.
Now we're going to turn that into separate terms.
We're going to get sqrt U + 9 / sqrt U all times DU.
And remember, we can think of this as U to the half +9 U to
the negative half.
So now we're going to add 1 to the exponent.
So we're going to get U to the three halves and then we're
going to divide by the new exponent or multiply by the
reciprocal.
So 2/3 going to add 1 to the exponent.
So U to the one half, divide by the new exponent or multiply by
2 / 1.
We're going to remember our plus C and then we're going to do a
sub back.
So we're going to get 2/3 the quantity X -, 9 to the three
halves plus eighteen X -, 9 to the 1/2 + C.