# Thread: [SOLVED] Simplifying/Factoring an equation

1. ## [SOLVED] Simplifying/Factoring an equation

Hi All,

I had the question to integrate $\int x \sqrt{2x+1} dx$ I've done the calculus bits, but I'm having trouble simplifying/factoring the algebra bits it to the correct answer.

My answer: $\frac{1}{10}{{(2x+1)}^{5/2}}-\frac{1}{6}{{(2x+1)}^{3/2}} + c$

The simplified answer: $\frac{1}{15}{{(2x+1)}^{3/2}}(3x-1) + c$

If anyone could show me the algebra steps to simplify it, or just give me a start of how to do it it would be much appreciated,

2. Originally Posted by Markus123
Hi All,

I had the question to integrate $\int x \sqrt{2x+1} dx$ I've done the calculus bits, but I'm having trouble simplifying/factoring the algebra bits it to the correct answer.

My answer: $\frac{1}{10}{{(2x+1)}^{5/2}}-\frac{1}{6}{{(2x+1)}^{3/2}} + c$

The simplified answer: $\frac{1}{15}{{(2x+1)}^{3/2}}(3x-1) + c$
If you use the index law to write $(2x+1)^{5/2} = (2x+1)(2x+1)^{3/2}$, then you get $\tfrac{1}{10}{{(2x+1)}^{5/2}}-\tfrac{1}{6}{{(2x+1)}^{3/2}} + c = (2x+1)^{3/2}\bigl(\tfrac1{10}(2x+1) - \tfrac16\bigr) + c$, and all you have to do is simplify the contents of that bracket.

3. Great, thanks!