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Step-by-step Solution

Integral of $\frac{x+1}{x^2}$ with respect to x

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Answer

$\ln\left|x\right|-x^{-1}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{x+1}{x^2}dx$
1

Split the fraction $\frac{x+1}{x^2}$ in two terms with common denominator ($x^2$)

$\int\left(\frac{x}{x^2}+\frac{1}{x^2}\right)dx$
2

Simplifying the fraction by $x$

$\int\left(\frac{1}{x}+\frac{1}{x^2}\right)dx$

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Answer

$\ln\left|x\right|-x^{-1}+C_0$
$\int\frac{x+1}{x^2}dx$

Main topic:

Integrals of Rational Functions

Used formulas:

12. See formulas

Time to solve it:

~ 0.78 seconds