Notes in 01凑微分法

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Published	10/05/2024	凑微分法描述若\(\displaystyle\int f(u) \mathrm{d} u=F(u)+C\),且\(\varphi(x)\)可导,则\(\displaystyle\int f(\varphi(x)) \varphi^{\prime}(x) \mathrm{d} x=\text{____…
Published	10/05/2024	凑微分法2\(\displaystyle\int f\left(a x^{n}+b\right) x^{n-1} \mathrm{~d} x=\text{______.}\)
Published	10/05/2024	凑微分法3\(\displaystyle\int \frac{f(\sqrt{x})}{2 \sqrt{x}} \mathrm{~d} x=\text{______.}\)
Published	10/05/2024	凑微分法4\(\displaystyle\int \frac{1}{x^{2}} f\left(\frac{1}{x}\right) \mathrm{d} x=\text{______.}\)
Published	10/05/2024	凑微分法5\(\displaystyle\int \mathrm{e}^{x} f\left(\mathrm{e}^{x}\right) \mathrm{d} x=\text{______.}\)
Published	10/05/2024	凑微分法6\(\displaystyle\displaystyle\int \frac{f(\ln x)}{x} \mathrm{~d} x=\text{______.}\)
Published	10/05/2024	凑微分法7\(\displaystyle\int\left(1-\frac{1}{x^{2}}\right) f\left(x+\frac{1}{x}\right) \mathrm{d} x=\text{______.}\)
Published	10/05/2024	凑微分法8\(\displaystyle\int\left(1+\frac{1}{x^{2}}\right) f\left(x-\frac{1}{x}\right) \mathrm{d} x=\text{______.}\)
Published	10/05/2024	凑微分法9\(\displaystyle\int(1+\ln x) f(x \ln x) \mathrm{d} x=\text{______.}\)
Published	10/05/2024	凑微分法10\(\displaystyle\int f(\sin x) \cos x \mathrm{~d} x=\text{______.}\)
Published	10/05/2024	凑微分法11\(\displaystyle\int f(\cos x) \sin x \mathrm{~d} x=\text{______.}\)
Published	10/05/2024	凑微分法12\(\displaystyle\int f(\tan x) \sec ^{2} x \mathrm{~d} x=\text{______.}\)
Published	10/05/2024	凑微分法13\(\displaystyle\int f(\cot x) \csc ^{2} x \mathrm{~d} x=\text{______.}\)
Published	10/05/2024	凑微分法14\(\displaystyle\int f(\sec x) \sec x \tan x \mathrm{~d} x=\text{______.}\)
Published	10/05/2024	凑微分法15\(\displaystyle\int f(\csc x) \csc x \cot x \mathrm{~d} x=\text{______.}\)
Published	10/05/2024	凑微分法16\(\displaystyle\int \frac{f(\arcsin x)}{\sqrt{1-x^{2}}} \mathrm{~d} x=\text{______.}\)
Published	10/05/2024	凑微分法17\(\displaystyle\int \frac{f(\arctan x)}{1+x^{2}} \mathrm{~d} x=\text{______.}\)
Published	10/05/2024	序号第一类换元积分法公式表格1 第一类换元法 (凑微分法)若 \(\displaystyle\int f(u) \mathrm{d} u=F(u)+C\), 且 \(\varphi(x)\) 可导, 则\(\displaystyle\int f(\varphi(x)) \varphi^{\…
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