Integrace pomocí přímých metod
Urči pomocí přímé metody následující integrál:
\large{{\displaystyle\int\Large\frac{\left( x-1 \right) ^2}{x^3}d{}x}}
\large{{\displaystyle\int\Large\frac{\left( x-1 \right) ^2}{x^3}d{}x=\ln\left|x\right|-\left(-\frac{2}{x}\right)+\left(-\frac{1}{3x^2}\right)+C=\ln\left|x\right|+\frac{2}{x}-\frac{1}{3x^2}+C}}
\large{{\displaystyle\int\Large\frac{\left( x-1 \right) ^2}{x^3}d{}x=\ln\left|x\right|-\left(-\frac{1}{x}\right)+\left(-\frac{1}{2x^2}\right)+C=\ln\left|x\right|+\frac{1}{x}-\frac{1}{2x^2}+C}}
\large{{\displaystyle\int\Large\frac{\left( x-1 \right) ^2}{x^3}d{}x=\ln\left|x\right|-\left(-\frac{3}{x}\right)+\left(-\frac{1}{2x^2}\right)+C=\ln\left|x\right|+\frac{3}{x}-\frac{1}{2x^2}+C}}
\large{{\displaystyle\int\Large\frac{\left( x-1 \right) ^2}{x^3}d{}x=\ln\left|x\right|-\left(-\frac{2}{x}\right)+\left(-\frac{1}{2x^2}\right)+C=\ln\left|x\right|+\frac{2}{x}-\frac{1}{2x^2}+C}}