# Integration problem, stuck, not sure

• July 10th 2011, 11:58 AM
Integration problem, stuck, not sure
Hello,
Covering the topic of Indefinite Integral:

I am doing a question, which my book does not give the answer and hoping someone can look at it and tell me if I did this right.

Integre/sign then ( x^2 + 4x + 4 ) ^ 1/3 dx

So I worked out 1/3 to the numbers in the brackets.
So I have Int Sign ( x^7/3 + 4 x^4/3 + 4^1/3)
then:
int sign x^7/3 dx + 4 intsign x^4/3 dx + 4^1/3 intsign dx
3/10 x^10/2 + 12/7 x^7/3 + 4^1/3 x + C.

is this correct? or not, thanks.
Joanne
• July 10th 2011, 12:19 PM
kalyanram
Re: Integration problem, stuck, not sure
Quote:

So I worked out 1/3 to the numbers in the brackets.
So I have Int Sign ( x^7/3 + 4 x^4/3 + 4^1/3)
This is wrong as a polynomial cannot be broken down the way you have assumed it to.

This is how you can go about doing it $x^2 + 4x + 4 = (x+2)^2$ so you are expected to evaluate
$\int{((x+2)^2})^{\frac{1}{3}}dx} \Rightarrow \int{(x+2)^{\frac{2}{3}} dx}$ substitute $t= x+2$ and finish you integral.

Kalyan
• July 10th 2011, 03:44 PM
Re: Integration problem, stuck, not sure
3/5(x+2)^5/3 + C ??

Thanks for the help, and correcting me as well.
• July 10th 2011, 05:53 PM
skeeter
Re: Integration problem, stuck, not sure
Quote: