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