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# Maths C3 integration watch

1. There are a few integration questions in my textbook I couldn't do. I've worked most of them the whole way through, but I can't get the right answers. Here is one of them.

Integrate x/(sqrt(x+9)) using the substitution u=x+9.
The answer in the back of the book is 2/3(x+9)^0.5 (x-18) +c
To clarify, that's x+9 raised to the power of 1/2, multiplied by 2/3 and by x-18.

My workings:
du/dx = 1, du=dx
Integral of x/sqrt u
x=u-9
integral of (u-9)u^-0.5
Expanding the brackets I got the integral of u^0.5 - 9u^-0.5
Integrating that, I got 2/3 u^1.5 - 18u^0.5
which is 2/3(x+9)^1.5 - 18(x+9)^0.5
(I'm using decimals in the powers because it's a little bit clearer.)

I can see the right numbers in there, but otherwise it's not even similar to the answer. What am I doing wrong?

Thanks!
2. (Original post by JustJusty)
There are a few integration questions in my textbook I couldn't do. I've worked most of them the whole way through, but I can't get the right answers. Here is one of them.

Integrate x/(sqrt(x+9)) using the substitution u=x+9.
The answer in the back of the book is 2/3(x+9)^0.5 (x-18) +c
To clarify, that's x+9 raised to the power of 1/2, multiplied by 2/3 and by x-18.

My workings:
du/dx = 1, du=dx
Integral of x/sqrt u
x=u-9
integral of (u-9)u^-0.5
Expanding the brackets I got the integral of u^0.5 - 9u^-0.5
Integrating that, I got 2/3 u^1.5 - 18u^0.5
which is 2/3(x+9)^1.5 - 18(x+9)^0.5
(I'm using decimals in the powers because it's a little bit clearer.)

I can see the right numbers in there, but otherwise it's not even similar to the answer. What am I doing wrong?

Thanks!
You've done nothing wrong apart from the arbitrary constant, factorise, the answer in the book is a factorised version of your answer.
3. (Original post by NotNotBatman)
You've done nothing wrong apart from the arbitrary constant, factorise, the answer is the book is a factorised version of your answer.
Ah, yes, that makes sense. Thank you!

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