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

So my answer is

3/10 x^10/2 + 12/7 x^7/3 + 4^1/3 x + C.

is this correct? or not, thanks.

Joanne

Re: Integration problem, stuck, not sure

Hi Brady,

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 $\displaystyle x^2 + 4x + 4 = (x+2)^2$ so you are expected to evaluate

$\displaystyle \int{((x+2)^2})^{\frac{1}{3}}dx} \Rightarrow \int{(x+2)^{\frac{2}{3}} dx}$ substitute $\displaystyle t= x+2$ and finish you integral.

Kalyan

Re: Integration problem, stuck, not sure

So is the answer

3/5(x+2)^5/3 + C ??

Thanks for the help, and correcting me as well.

Re: Integration problem, stuck, not sure

Quote:

Originally Posted by

**bradycat** So is the answer

3/5(x+2)^5/3 + C ??

Thanks for the help, and correcting me as well.

check the validity of an antiderivative by taking the derivative of your solution ...

Re: Integration problem, stuck, not sure

Oh I forgot about that, ya it's correct then.

Thanks

Joanne