1. ## integration by substitution

int(cuberoot(x^3+1)x^5dx

2. Originally Posted by samdmansam
int(cuberoot(x^3+1)x^5dx
please clarify, you are missing some parenthesis. do you mean $\displaystyle \int \sqrt[3]{x^3 + 1} \cdot x^5~dx$ ?

3. ## Int by substitution

Originally Posted by Jhevon
please clarify, you are missing some parenthesis. do you mean $\displaystyle \int \sqrt[3]{x^3 + 1} \cdot x^5~dx$ ?
yes thats exactly what I meant, Thanks

4. Originally Posted by samdmansam
yes thats exactly what I meant, Thanks
ok, well integration by substitution will work nicely. make a substitution of $\displaystyle u = x^3 + 1$ (and note that $\displaystyle x^5 = x^3 \cdot x^2$)

5. Make $\displaystyle z^3=x^3+1\implies z^2\,dz=x^2\,dx,$ it's a more direct way to solve the problem, you get rid of the cube root.

6. ## could you please take it a little further

my text has very basic examples then skips to questions with cuberoots