Find the integral int(8/(5-2x))dx

 Exercise

$\int\frac{8}{5-2x}dx$

 

The integral of a function times a constant ($8$) is equal to the constant times the integral of the function

$8\int\frac{1}{5-2x}dx$

 

Apply the formula: $\int\frac{n}{ax+b}dx$$=\frac{n}{a}\ln\left(ax+b\right)+C$, where $a=-2$, $b=5$ and $n=1$

$8\cdot \left(\frac{1}{-2}\right)\ln\left|-2x+5\right|$

 

Multiply the fraction and term in $8\cdot \left(\frac{1}{-2}\right)\ln\left|-2x+5\right|$

$-4\ln\left|-2x+5\right|$

 

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$-4\ln\left|-2x+5\right|+C_0$

$-4\ln\left|-2x+5\right|+C_0$

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