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$$$717897987691852588770249 x^{50}$$$の積分
入力内容
$$$\int 717897987691852588770249 x^{50}\, dx$$$ を求めよ。
解答
定数倍の法則 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ を、$$$c=717897987691852588770249$$$ と $$$f{\left(x \right)} = x^{50}$$$ に対して適用する:
$${\color{red}{\int{717897987691852588770249 x^{50} d x}}} = {\color{red}{\left(717897987691852588770249 \int{x^{50} d x}\right)}}$$
$$$n=50$$$ を用いて、べき乗の法則 $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ を適用します:
$$717897987691852588770249 {\color{red}{\int{x^{50} d x}}}=717897987691852588770249 {\color{red}{\frac{x^{1 + 50}}{1 + 50}}}=717897987691852588770249 {\color{red}{\left(\frac{x^{51}}{51}\right)}}$$
したがって、
$$\int{717897987691852588770249 x^{50} d x} = \frac{239299329230617529590083 x^{51}}{17}$$
積分定数を加える:
$$\int{717897987691852588770249 x^{50} d x} = \frac{239299329230617529590083 x^{51}}{17}+C$$
解答
$$$\int 717897987691852588770249 x^{50}\, dx = \frac{239299329230617529590083 x^{51}}{17} + C$$$A