Question

Number 2, find the most general anti-derivative. See attachment.

Answer 1

try spliting up the sum and simplfying the terms to powers

Answer 2

or you could factor ou the root x and simplify to clear it up a bit more

Answer 3

\[={x^{\frac{3}{2}}+x^{\frac{1}{2}} \over x^2}=x^{-\frac{1}{2}}+x^{-\frac{3}{2}}\]

Answer 4

Now integrate this (find its anti-derivative) using the power rule, which I think you know.

Answer 5

Umm, would it be \[2(x-1)/\sqrt{x}+C\]

Answer 6

\[\int f(x)+g(x)dx=\int f(x)dx+\int g(x)dx\]
\[\int x^Pdx=\frac{1}{P+1}\ x^{P+1}\]