# Factorization Calculator

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### Difficult Problems

1

Example

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

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

$\int\left(\frac{1}{x}+\frac{x^2}{x}\right)dx$
3

Simplifying the fraction by $x$

$\int\left(\frac{1}{x}+x\right)dx$
4

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int\frac{1}{x}dx+\int xdx$
5

Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$\int\frac{1}{x}dx+\frac{1}{2}x^2$
6

The integral of the inverse of the lineal function is given by the following formula, $\displaystyle\int\frac{1}{x}dx=\ln(x)$

$\ln\left|x\right|+\frac{1}{2}x^2$
7

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