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