# Math virtual assistant

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# Step-by-step Solution

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## Answer

$\frac{-\frac{1}{8}}{x-1}+\frac{\frac{1}{8}}{x+3}+C_0$

## Step-by-step explanation

Problem to solve:

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

Split the fraction $\frac{x+1}{\left(x^2+2x-3\right)^2}$ in two terms with common denominator ($\left(x^2+2x-3\right)^2$)

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

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

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

## Answer

$\frac{-\frac{1}{8}}{x-1}+\frac{\frac{1}{8}}{x+3}+C_0$
$\int\frac{\left(X+1\right)}{\left(X^2+2X-3\right)^2}dx$

### Main topic:

Integrals of Rational Functions

11. See formulas

~ 1.22 seconds