$$$2 x \ln\left(9\right)$$$ 的积分
您的输入
求$$$\int 2 x \ln\left(9\right)\, dx$$$。
解答
对 $$$c=2 \ln{\left(9 \right)}$$$ 和 $$$f{\left(x \right)} = x$$$ 应用常数倍法则 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$：
$${\color{red}{\int{2 x \ln{\left(9 \right)} d x}}} = {\color{red}{\left(2 \ln{\left(9 \right)} \int{x d x}\right)}}$$
应用幂法则 $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$，其中 $$$n=1$$$：
$$2 \ln{\left(9 \right)} {\color{red}{\int{x d x}}}=2 \ln{\left(9 \right)} {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}=2 \ln{\left(9 \right)} {\color{red}{\left(\frac{x^{2}}{2}\right)}}$$
因此，
$$\int{2 x \ln{\left(9 \right)} d x} = x^{2} \ln{\left(9 \right)}$$
化简：
$$\int{2 x \ln{\left(9 \right)} d x} = 2 x^{2} \ln{\left(3 \right)}$$
加上积分常数：
$$\int{2 x \ln{\left(9 \right)} d x} = 2 x^{2} \ln{\left(3 \right)}+C$$
答案
$$$\int 2 x \ln\left(9\right)\, dx = 2 x^{2} \ln\left(3\right) + C$$$A