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Integral dari $$$\theta \tan{\left(2 \right)}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \theta \tan{\left(2 \right)}\, d\theta$$$.
Solusi
Terapkan aturan pengali konstanta $$$\int c f{\left(\theta \right)}\, d\theta = c \int f{\left(\theta \right)}\, d\theta$$$ dengan $$$c=\tan{\left(2 \right)}$$$ dan $$$f{\left(\theta \right)} = \theta$$$:
$${\color{red}{\int{\theta \tan{\left(2 \right)} d \theta}}} = {\color{red}{\tan{\left(2 \right)} \int{\theta d \theta}}}$$
Terapkan aturan pangkat $$$\int \theta^{n}\, d\theta = \frac{\theta^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=1$$$:
$$\tan{\left(2 \right)} {\color{red}{\int{\theta d \theta}}}=\tan{\left(2 \right)} {\color{red}{\frac{\theta^{1 + 1}}{1 + 1}}}=\tan{\left(2 \right)} {\color{red}{\left(\frac{\theta^{2}}{2}\right)}}$$
Oleh karena itu,
$$\int{\theta \tan{\left(2 \right)} d \theta} = \frac{\theta^{2} \tan{\left(2 \right)}}{2}$$
Tambahkan konstanta integrasi:
$$\int{\theta \tan{\left(2 \right)} d \theta} = \frac{\theta^{2} \tan{\left(2 \right)}}{2}+C$$
Jawaban
$$$\int \theta \tan{\left(2 \right)}\, d\theta = \frac{\theta^{2} \tan{\left(2 \right)}}{2} + C$$$A