Metoda substituce pro primitivní funkci
Metodou substituce urči primitivní funkci k následující funkci:
\large f\left( x\right) = \cos {\left( 3x+5 \right) }
\large{{{{{{{{\displaystyle\int\Large\frac{\cos{u}}{3}d{}\:u=\frac{1}{3}{{{{{\displaystyle\int\cos\:{ud}{}\:u=\frac{1}{3}\large\cdot\sin{u}+C=\frac{1}{3}\cdot\sin{\left( 3x+5 \right) }+C}}}}}}}}}}}}}
\large{{{{{{{{\displaystyle\int\Large\frac{\cos{u}}{4}d{}\:u=\frac{1}{4}{{{{{\displaystyle\int\cos\:{ud}{}\:u=\frac{1}{4}\large\cdot\sin{u}+C=\frac{1}{4}\cdot\sin{\left( 3x+5 \right) }+C}}}}}}}}}}}}}
\large{{{{{{{{\displaystyle\int\Large\frac{\cos{u}}{3}d{}\:u=\frac{1}{3}{{{{{\displaystyle\int\cos\:{ud}{}\:u=\frac{1}{3}\large\cdot\sin{u}+C=\frac{1}{3}\cdot\sin{\left( 3x+4 \right) }+C}}}}}}}}}}}}}
\large{{{{{{{{\displaystyle\int\Large\frac{\sin{u}}{3}d{}\:u=\frac{1}{3}{{{{{\displaystyle\int\sin\:{ud}{}\:u=\frac{1}{3}\large\cdot\cos{u}+C=\frac{1}{3}\cdot\cos{\left( 3x+5 \right) }+C}}}}}}}}}}}}}