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