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Method of substitution

$$ \int f\left(g(x)\right)\cdot g'(x) dx = \int f(u) du $$ 
Integration by parts

$$ \int f(x) \cdot g'(x)dx = f(x) \cdot g(x)  \int g(x) \cdot f'(x)dx $$ 

$$ \int x^n dx = \frac{x^{n+1}}{n+1} + C , n \ne 1 $$ 

$$ \int \frac{1}{x} dx = \lnx + C $$ 

$$ \int c \, dx = c \cdot x + C $$ 

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

$$ \int x^2 \, dx = \frac{x^3}{3} + C $$ 

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

$$ \int \sqrt{x} \, dx = \frac{2\cdot x \cdot \sqrt{x} }{3} + C $$ 

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

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

$$ \int \sin x\,dx = \cos x + C $$ 

$$ \int \cos x\,dx = \sin x + C $$ 

$$ \int \tan x\,dx = \ln\sec x + C $$ 

$$ \int \sec x\,dx = \ln\tan x + \sec x  + C $$ 

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

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

$$ \int \tan^2x\,dx = \tan x  x + C $$ 

$$ \int \sec^2x\,dx = \tan x + C $$ 

$$ \int \ln x \,dx =x \cdot \ln x x + C $$ 

$$ \int x^n \cdot \ln x \,dx =\frac{x^{n+1}}{n+1} \ln x  \frac{x^{n+1}}{(n+1)^2} + C $$ 

$$ \int e^x\,dx = e^x + C $$ 

$$ \int a^x\,dx = \frac{a^x}{\ln a} + C $$ 
Please tell me how can I make this better.