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5-5-43 usub
X
    00:00 / 00:00
    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.