Integral dari $$$- 2 x^{3} \sin{\left(1 \right)}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \left(- 2 x^{3} \sin{\left(1 \right)}\right)\, dx$$$.
Solusi
Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=- 2 \sin{\left(1 \right)}$$$ dan $$$f{\left(x \right)} = x^{3}$$$:
$${\color{red}{\int{\left(- 2 x^{3} \sin{\left(1 \right)}\right)d x}}} = {\color{red}{\left(- 2 \sin{\left(1 \right)} \int{x^{3} d x}\right)}}$$
Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=3$$$:
$$- 2 \sin{\left(1 \right)} {\color{red}{\int{x^{3} d x}}}=- 2 \sin{\left(1 \right)} {\color{red}{\frac{x^{1 + 3}}{1 + 3}}}=- 2 \sin{\left(1 \right)} {\color{red}{\left(\frac{x^{4}}{4}\right)}}$$
Oleh karena itu,
$$\int{\left(- 2 x^{3} \sin{\left(1 \right)}\right)d x} = - \frac{x^{4} \sin{\left(1 \right)}}{2}$$
Tambahkan konstanta integrasi:
$$\int{\left(- 2 x^{3} \sin{\left(1 \right)}\right)d x} = - \frac{x^{4} \sin{\left(1 \right)}}{2}+C$$
Jawaban
$$$\int \left(- 2 x^{3} \sin{\left(1 \right)}\right)\, dx = - \frac{x^{4} \sin{\left(1 \right)}}{2} + C$$$A