Integration by Substitution: What Went Wrong in Solving \int x(x^{2}+5)^{75} dx?

[Stratosphere]

Homework Statement

I've come across the problem
$$\ \int x(x^{2}+5)^{75} dx$$

Homework Equations

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?

 

[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

 

[HallsofIvy]

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

 

[Stratosphere]

Oh, now I see, thanks.