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$$$\frac{75 i d n t x^{32}}{p^{2}}$$$ 关于$$$x$$$的积分
您的输入
求$$$\int \frac{75 i d n t x^{32}}{p^{2}}\, dx$$$。
解答
对 $$$c=\frac{75 i d n t}{p^{2}}$$$ 和 $$$f{\left(x \right)} = x^{32}$$$ 应用常数倍法则 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$：
$${\color{red}{\int{\frac{75 i d n t x^{32}}{p^{2}} d x}}} = {\color{red}{\left(\frac{75 i d n t \int{x^{32} d x}}{p^{2}}\right)}}$$
应用幂法则 $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$，其中 $$$n=32$$$：
$$\frac{75 i d n t {\color{red}{\int{x^{32} d x}}}}{p^{2}}=\frac{75 i d n t {\color{red}{\frac{x^{1 + 32}}{1 + 32}}}}{p^{2}}=\frac{75 i d n t {\color{red}{\left(\frac{x^{33}}{33}\right)}}}{p^{2}}$$
因此，
$$\int{\frac{75 i d n t x^{32}}{p^{2}} d x} = \frac{25 i d n t x^{33}}{11 p^{2}}$$
加上积分常数：
$$\int{\frac{75 i d n t x^{32}}{p^{2}} d x} = \frac{25 i d n t x^{33}}{11 p^{2}}+C$$
答案
$$$\int \frac{75 i d n t x^{32}}{p^{2}}\, dx = \frac{25 i d n t x^{33}}{11 p^{2}} + C$$$A