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Integraal van $$$\frac{f_{1} \tan^{2}{\left(f \right)}}{g}$$$ met betrekking tot $$$g$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int \frac{f_{1} \tan^{2}{\left(f \right)}}{g}\, dg$$$.
Oplossing
Pas de constante-veelvoudregel $$$\int c f{\left(g \right)}\, dg = c \int f{\left(g \right)}\, dg$$$ toe met $$$c=f_{1} \tan^{2}{\left(f \right)}$$$ en $$$f{\left(g \right)} = \frac{1}{g}$$$:
$${\color{red}{\int{\frac{f_{1} \tan^{2}{\left(f \right)}}{g} d g}}} = {\color{red}{f_{1} \tan^{2}{\left(f \right)} \int{\frac{1}{g} d g}}}$$
De integraal van $$$\frac{1}{g}$$$ is $$$\int{\frac{1}{g} d g} = \ln{\left(\left|{g}\right| \right)}$$$:
$$f_{1} \tan^{2}{\left(f \right)} {\color{red}{\int{\frac{1}{g} d g}}} = f_{1} \tan^{2}{\left(f \right)} {\color{red}{\ln{\left(\left|{g}\right| \right)}}}$$
Dus,
$$\int{\frac{f_{1} \tan^{2}{\left(f \right)}}{g} d g} = f_{1} \ln{\left(\left|{g}\right| \right)} \tan^{2}{\left(f \right)}$$
Voeg de integratieconstante toe:
$$\int{\frac{f_{1} \tan^{2}{\left(f \right)}}{g} d g} = f_{1} \ln{\left(\left|{g}\right| \right)} \tan^{2}{\left(f \right)}+C$$
Antwoord
$$$\int \frac{f_{1} \tan^{2}{\left(f \right)}}{g}\, dg = f_{1} \ln\left(\left|{g}\right|\right) \tan^{2}{\left(f \right)} + C$$$A