# Math Help - integral - can someone explain this question step by step plz and thank you

1. ## integral - can someone explain this question step by step plz and thank you

(x^4+1)^8 4x^3

i know what the answer is , i just want to see how to do it

2. Maybe by putting $u=x^4+1$ and $du=4x^3$.
So you have $\int u^8 du$.

3. Originally Posted by rock candy
(x^4+1)^8 4x^3

i know what the answer is , i just want to see how to do it
$I = \int (x^4+1)^8 \times 4x^3 dx$

$\text{Let } u = x^4 + 1$

$\text{Then } \frac{du}{dx} = 4x^3$

$\therefore du = 4x^3 dx$

$\text{Hence } I = \int u^8 du = \frac{u^9}{9} + C = (x^4+1)^9 + C$

4. thanks for clearing that up ... i should of seen that .. i guess im sleepy

5. It's actually $\frac{(x^4+1)^9}{9} + C$. You forgot to keep the $9$ in the denominator when you subbed back in.