Question

integrate( 2x^2-1)÷x(x^2-logx​

Answer 1

Step-by-step explanation:

Given to integrate (2x²-1)/x(x²-logx)

Now,

$\int \frac{(2 {x}^{2} - 1)dx}{x( {x}^{2} - log(x)) }$

$= \int \frac{ (\frac{2{x}^{2} - 1 }{x}) dx}{ {x}^{2} - log(x) )}$

$= \int \frac{(2x - \frac{1}{x} )dx}{ ({x}^{2} - log(x)) }$

Let, x² - log(x)=t

=>(2x - 1/x)dx = dt

so,

$= \int \frac{dt}{t}$

$= ln \: |t|+ c$

$= ln \: | {x}^{2} - log(x) | + c$