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$$$717897987691852588770249 x^{50}$$$ 的积分
您的输入
求$$$\int 717897987691852588770249 x^{50}\, dx$$$。
解答
对 $$$c=717897987691852588770249$$$ 和 $$$f{\left(x \right)} = x^{50}$$$ 应用常数倍法则 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$：
$${\color{red}{\int{717897987691852588770249 x^{50} d x}}} = {\color{red}{\left(717897987691852588770249 \int{x^{50} d x}\right)}}$$
应用幂法则 $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$，其中 $$$n=50$$$：
$$717897987691852588770249 {\color{red}{\int{x^{50} d x}}}=717897987691852588770249 {\color{red}{\frac{x^{1 + 50}}{1 + 50}}}=717897987691852588770249 {\color{red}{\left(\frac{x^{51}}{51}\right)}}$$
因此，
$$\int{717897987691852588770249 x^{50} d x} = \frac{239299329230617529590083 x^{51}}{17}$$
加上积分常数：
$$\int{717897987691852588770249 x^{50} d x} = \frac{239299329230617529590083 x^{51}}{17}+C$$
答案
$$$\int 717897987691852588770249 x^{50}\, dx = \frac{239299329230617529590083 x^{51}}{17} + C$$$A