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Integral dari $$$3 x^{5} \cos{\left(3 \right)}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int 3 x^{5} \cos{\left(3 \right)}\, dx$$$.
Solusi
Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=3 \cos{\left(3 \right)}$$$ dan $$$f{\left(x \right)} = x^{5}$$$:
$${\color{red}{\int{3 x^{5} \cos{\left(3 \right)} d x}}} = {\color{red}{\left(3 \cos{\left(3 \right)} \int{x^{5} d x}\right)}}$$
Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=5$$$:
$$3 \cos{\left(3 \right)} {\color{red}{\int{x^{5} d x}}}=3 \cos{\left(3 \right)} {\color{red}{\frac{x^{1 + 5}}{1 + 5}}}=3 \cos{\left(3 \right)} {\color{red}{\left(\frac{x^{6}}{6}\right)}}$$
Oleh karena itu,
$$\int{3 x^{5} \cos{\left(3 \right)} d x} = \frac{x^{6} \cos{\left(3 \right)}}{2}$$
Tambahkan konstanta integrasi:
$$\int{3 x^{5} \cos{\left(3 \right)} d x} = \frac{x^{6} \cos{\left(3 \right)}}{2}+C$$
Jawaban
$$$\int 3 x^{5} \cos{\left(3 \right)}\, dx = \frac{x^{6} \cos{\left(3 \right)}}{2} + C$$$A