How did they do this?

[Superposed_Cat]

http://tutorial.math.lamar.edu/Classes/CalcI/ComputingIndefiniteIntegrals_files/eq0020MP.gif I get how they integrating but I don't get how they simplified the last term.

 

[Mark44]

http://tutorial.math.lamar.edu/Classes/CalcI/ComputingIndefiniteIntegrals_files/eq0020MP.gif I get how they integrating but I don't get how they simplified the last term.

Are you stumped by the arithmetic with fractions?

$$ \frac{1}{\frac{7}{4}} = \frac 4 7$$
Now multiply by 3. What do you get?

6 * 1/2 = ?

 

[Superposed_Cat]

No with this, but my algebra is terrible and I haven't had to use fractions properly for ages as I always usually convert to decimals.

 

[Mark44]

No with this, but my algebra is terrible

This isn't even algebra - it's arithmetic, and about 6th grade at that.

and I haven't had to use fractions properly for ages as I always usually convert to decimals.

Then it would behoove you to brush up on arithmetic involving fractions. Some time spent going through some videos at khanacademy (http://www.khanacademy.org/math/cc-sixth-grade-math) would be a very good investment.

 

[Astrum]

No with this, but my algebra is terrible and I haven't had to use fractions properly for ages as I always usually convert to decimals.

That's just saying that $$\frac{1}{6}\int x^{-1/2}dx = \frac{1}{6}[2x^{1/2}]$$

You're aware of the generic formula: $\int x^n dx = \frac{1}{n+1}x^{n+1}$ right?