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\int\frac{2x-1}{\left(x+1\right)\left(x-6\right)}dx

Integral of (2x-1)/((x+1)(x-6))

Answer

$\frac{11}{7}\ln\left|x-6\right|+\frac{3}{7}\ln\left|1+x\right|+C_0$

Step-by-step explanation

Problem

$\int\frac{2x-1}{\left(x+1\right)\left(x-6\right)}dx$
1

Using partial fraction decomposition, the fraction $\frac{2x-1}{\left(x-6\right)\left(1+x\right)}$ can be rewritten as

$\frac{2x-1}{\left(x-6\right)\left(1+x\right)}=\frac{A}{x-6}+\frac{B}{1+x}$

Unlock this step-by-step solution!

Answer

$\frac{11}{7}\ln\left|x-6\right|+\frac{3}{7}\ln\left|1+x\right|+C_0$

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$\int\frac{2x-1}{\left(x+1\right)\left(x-6\right)}dx$

Main topic:

Integrals by partial fraction expansion

Used formulas:

5. See formulas

Time to solve it:

~ 0.45 seconds