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\int\frac{1}{x^2+2x-3}dx

Integral of 1/(2x-3+x^2)

Answer

$-\frac{1}{4}\ln\left|3+x\right|+\frac{1}{4}\ln\left|x-1\right|+C_0$

Step-by-step explanation

Problem

$\int\frac{1}{x^2+2x-3}dx$
1

Factor the trinomial $-3+2x+x^2$ finding two numbers that multiply to form $-3$ and added form $2$

$\begin{matrix}\left(-1\right)\left(3\right)=-3\\ \left(-1\right)+\left(3\right)=2\end{matrix}$

Unlock this step-by-step solution!

Answer

$-\frac{1}{4}\ln\left|3+x\right|+\frac{1}{4}\ln\left|x-1\right|+C_0$
$\int\frac{1}{x^2+2x-3}dx$

Main topic:

Integrals by partial fraction expansion

Used formulas:

6. See formulas

Time to solve it:

~ 0.95 seconds