Ejercicio
$\log\frac{\left(x\left(x+2\right)\right)}{\left(x+3\right)^2}$
Derivada de esta función
$\frac{d}{dx}\left(\log \left(\frac{x\left(x+2\right)}{\left(x+3\right)^2}\right)\right)=\frac{\left(x+2+x\right)\left(x+3\right)^2+2\left(-x-2\right)x\left(x+3\right)}{\ln\left(10\right)x\left(x+2\right)\left(x+3\right)^{2}}$
Ver solución paso a paso
Integral de esta función
$\int\log \left(\frac{x\left(x+2\right)}{\left(x+3\right)^2}\right)dx=\frac{-2\ln\left(x+3-1\right)}{\ln\left(10\right)}+\frac{4\ln\left(x+3-1\right)}{\ln\left(10\right)}+\frac{-2\left(x+2\right)}{\ln\left(10\right)}+\frac{x\ln\left(x\left(x+2\right)\right)}{\ln\left(10\right)}+\frac{2\left(x+3\right)}{\ln\left(10\right)}+\frac{-2\left(x+3\right)\ln\left(x+3\right)}{\ln\left(10\right)}+C_0$
Ver solución paso a paso