Evaluate the Integral

Question

Evaluate the integral  .

Question options:

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Answer 1

So I should preface this with was not able to get one of the answer choices. I hope someone can see my error or maybe the answer is not an option.

First I want to choose 1 - x as my u

u = 1 - x

then find du

du = -1

To solve this we will also need to find x

u = 1 - x

x = 1 - u

With this we will substitute back into the integral

int( (1 - u) (u)^(1/2) (-1du)

Next we will pull the negative 1 out in front of the integral as it is a constant. We will also distribute the u^(1/2)

-int( (u^(1/2)) - (u^(3/2)) du)

Next take the integral and add the integral constant

-[ 2/3(u^(3/2)) - 2/5(u^(5/2)) ] + C

Next distribute the negative and substitute 1 - x for u

2/5(1 - x)^(5/2) - 2/3(1 - x)^(3/2) + C