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Metoda substituce pro primitivní funkci
Metodou substituce urči primitivní funkci k následující funkci:
\large f\left( x\right) = \Large \frac{4x}{x^2+2}\large
\large{{{\displaystyle\int\Large\frac{2}{u}d{}u=2{\displaystyle\int\frac{1}{u}\large{d}u=2\cdot\ln{\left|u\right|}+C=2\cdot\ln{\left|x^2+3\right|}+C}}}}
\large{{{\displaystyle\int\Large\frac{2}{u}d{}u=2{\displaystyle\int\frac{1}{u}\large{d}u=2\cdot\ln{\left|u\right|}+C=2\cdot\ln{\left|x^2+4\right|}+C}}}}
\large{{{\displaystyle\int\Large\frac{2}{u}d{}u=2{\displaystyle\int\frac{1}{u}\large{d}u=2\cdot\ln{\left|u\right|}+C=2\cdot\ln{\left|x^2+2\right|}+C}}}}
\large{{{\displaystyle\int\Large\frac{2}{u}d{}u=2{\displaystyle\int\frac{1}{u}\large{d}u=2\cdot\ln{\left|u\right|}+C=2\cdot\ln{\left|x^2+1\right|}+C}}}}