Question

Can I get an answer to this question please c&d

Answer 1

As given by the question

There are given that the integration:

$\int \frac{5x+2}{(3x+4)(x-1)}dx$

Now,

First, take the partial fraction of the given integration:

$\frac{5x+2}{(3x+4)(x-1)}=\frac{2}{3x+4}+\frac{1}{x-1}$

Then,

$\begin{gathered} \int \frac{5x+2}{(3x+4)(x-1)}dx=\int \frac{2}{3x+4}+\frac{1}{x-1}dx \\ =\int \frac{2}{3x+4}dx+\int \frac{1}{x-1}dx \end{gathered}$

Then,

From the formula:

$\int \frac{2}{3x+4}dx+\int \frac{1}{x-1}dx=\frac{2}{3}\ln |3x+4++\ln |x-1|+c$

Hence, the value of the given integration is shown below:

$\int \frac{5x+2}{(3x+4)(x-1)}dx=\frac{2}{3}\ln |3x+4++\ln |x-1|+c$