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 (5x+2)/((3x+4)(x-1))dx`

Now,

First, take the partial fraction of the given integration:

`(5x+2)/((3x+4)(x-1))=(2)/(3x+4)+(1)/(x-1)`

Then,

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

Then,

From the formula:

`\int (2)/(3x+4)dx+\int (1)/(x-1)dx=(2)/(3)\ln |3x+4++\ln |x-1|+c`

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

`\int (5x+2)/((3x+4)(x-1))dx=(2)/(3)\ln |3x+4++\ln |x-1|+c`