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Metoda substituce v integraci
Metodou substituce urči primitivní funkci k následující funkci:
\large f\left( x\right) = \sqrt {x^2+3}\cdot 2x
\large \Large \frac{2 \left( x^2+3\right) ^{\frac{5}{2}}}{3}\large +C = \Large \frac{2}{3}\large \cdot \left( x^2+3 \right) \cdot \sqrt {x^2+3}+C
\large \Large \frac{2 \left( x^2+3\right) ^{\frac{3}{2}}}{5}\large +C = \Large \frac{2}{5}\large \cdot \left( x^2+3 \right) \cdot \sqrt {x^2+3}+C
\large \Large \frac{2 \left( x^2+3\right) ^{\frac{3}{2}}}{3}\large +C = \Large \frac{2}{3}\large \cdot \left( x^2+3 \right) \cdot \sqrt {x^2+3}+C
\large \Large \frac{3 \left( x^2+3\right) ^{\frac{3}{2}}}{2}\large +C = \Large \frac{3}{2}\large \cdot \left( x^2+3 \right) \cdot \sqrt {x^2+3}+C