# Evaluate the following integrals. Include absolute values only when needed. intfrac{ln^2x+2ln x-1}{x}dx

Evaluate the following integrals. Include absolute values only when needed.
$\int \frac{{\mathrm{ln}}^{2}x+2\mathrm{ln}x-1}{x}dx$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

SoosteethicU

$\text{we have to find the given integral.}$
$\text{here,}\int \frac{{\mathrm{ln}}^{2}x+2\mathrm{ln}x-1}{x}dx$

$⇒,\int \frac{{\mathrm{ln}}^{2}x+2\mathrm{ln}x-1}{x}dx=\int \left({t}^{2}+2t-1\right)dt$
$=\int {t}^{2}dt+2\int tdt-\int 1dt$
$=\frac{{t}^{3}}{3}+2\frac{{t}^{2}}{2}-t+C$
$=\frac{{t}^{3}}{3}+{t}^{2}-t+C$

$⇒\int \frac{{\mathrm{ln}}^{2}x+2\mathrm{ln}x-1}{x}dx=\frac{{\mathrm{ln}}^{3}x}{3}+{\mathrm{ln}}^{2}x-\mathrm{ln}x+C$
$\text{this is the required answer}$