# Integration by Substitution

1. Jul 25, 2009

### Stratosphere

1. The problem statement, all variables and given/known data
I've come across the problem
$$\ \int x(x^{2}+5)^{75} dx$$

2. Relevant equations

3. The attempt at a solution
Once going through the whole problem I got $$\ \frac{(x^{2}+5)^{76}}{76}+c$$
but the text I have said the answer was, $$\frac{1}{152}(x^{2}+5)^{76}+c$$.
What did I do wrong?

2. Jul 25, 2009

### VeeEight

Did you try differentiating the answers to see which one gives you $$x(x^{2}+5)^{75}$$ ? Remember to apply the chain rule and that differentiating $$x^{2}+5$$ gives 2x

3. Jul 26, 2009

### HallsofIvy

Staff Emeritus
Presumably you let u= x^2+ 5. Then du= 2x dx. You forgot the "2".

4. Jul 26, 2009

### Stratosphere

Oh, now I see, thanks.