Nguyên Hàm và Tích Phân

$$\int_{ }^{ }f(x)g(x)dx=f(x).\int_{ }^{ }g(x)dx$$

$$\int\frac{f(x)}{g(x)}dx=\frac{\int f(x)dx}{\int g(x)dx}.$$

$$\int[f(x)-g(x)]dx=\int f(x)dx-\int g(x)dx.$$

$$\int f(x).g(x)dx=f(x).\int g(x)dx.$$

$$\int\left[f(x).g(x)\right]dx=\int f(x)dx.\int g(x)dx,\ g(x)\ne0.$$

$$\int\left[f(x)+g(x)\right]dx=\int f(x)dx+\int g(x)dx.$$

$$\int\frac{f(x)}{g(x)}dx=\int f(x)dx-\int g(x)dx,\ g(x)\ne0.$$

$$\int\left(f(x).g(x)\right)dx=\int f(x)dx.\int g(x)dx.$$

$$\int kf(x)dx=k\int f(x)dx$$

$$\int kf(x)dx=\int f(x)dx$$

$$\int kf(x)dx=k-\int f(x)dx$$

$$\int kf(x)dx=\int[f(x)]^kdx$$

$$\int x^{\alpha}dx=\frac{x^{\alpha+1}}{\alpha+1}+C\ (\alpha\ne1)$$

$$\int x^{\alpha}dx=x^{\alpha}+C$$

$$\int x^{\alpha}dx=\alpha.x^{\alpha-1}+C$$

$$\int x^{\alpha}dx=x^{\alpha+1}+C$$

$$\int\sin xdx=\cos x+C$$

$$\int\sin xdx=-\cos x+C$$

$$\int\sin xdx=\tan x+C$$

$$\int\sin xdx=\sin x+C$$

$$\int\cos xdx=\sin x+C$$

$$\int\cos xdx=-\sin x+C$$

$$\int\cos xdx=\tan x+C$$

$$\int\sin xdx=-\cot x+C$$

$$\int\frac{1}{\cos^2x}dx=\cos x+C$$

$$\int\frac{1}{\cos^2x}dx=\sin x+C$$

$$\int\frac{1}{\cos^2x}dx=\tan x+C$$

$$\int\frac{1}{\cos^2x}dx=\cot x+C$$

$$\int\frac{1}{\sin^2x}dx=\cos x+C$$

$$\int\frac{1}{\sin^2x}dx=-\sin x+C$$

$$\int\frac{1}{\sin^2x}dx=-\tan x+C$$

$$\int\frac{1}{\sin^2x}dx=-\cot x+C$$

$$\int e^xdx=e^x+C$$

$$\int e^xdx=-e^x+C$$

$$\int e^xdx=xe^{x-1}+C$$

$$\int e^xdx=\frac{e^{x+1}}{x+1}+C$$

$$\int a^xdx=a^x+C$$

$$\int a^xdx=\frac{a^x}{\ln a}+C$$

$$\int a^xdx=xa^{x-1}+C$$

$$\int a^xdx=\frac{a^{x+1}}{x+1}+C$$