Question

Trig indefinite integral: (I'll type it)...

Answer 1

\[\int\limits_{}^{}\]\[\frac{ 3 }{ 2\sqrt{x}(1+x) }\]dx

Answer 2

Is partial fraction decomposition possible?

Answer 3

\[
\frac{3}{2\sqrt x(1+x)} = \frac{A}{2\sqrt x}+\frac{B}{1+x}
\]

Answer 4

I don't know what that is - I don't have examples in the book that are very similar

Answer 5

sorry if I'm slow to reply, my computer is being screwy. that looks helpful, let me work on it

Answer 6

\[
\begin{split}
\frac{3}{2\sqrt x(1+x)}
&= \frac{A}{2\sqrt x}+\frac{B}{1+x} \\
&= \frac{A(1+x)}{2\sqrt x(1+x)}+\frac{2B\sqrt x}{2\sqrt x(1+x)}
\end{split}
\implies
3= A(1+x)+2B\sqrt x
\]

Answer 7

I'm not sure this will work though. I'm just throwing out a possible method.

Answer 8

I don't understand what A and B mean and how I would go about solving for them/getting rid of them