1) $\int{[f_1(x)\pm f_2(x)]}dx= \int{f_1(x)}dx \pm \int{f_2(x)}dx $
2) $\int{k \cdot f(x)}dx =k \cdot \int{f(x)}dx $
where k is constant.
3) $\int{[k_1f_1(x)\pm k_2f_2(x)]}dx= k_1\int{f_1(x)}dx \pm k_2 \int{f_2}dx $
4) If $f(x)dx=g(x)+c $ , then $\int{f(ax+b)}dx= \frac{1}{a}g(ax+b)+c $
Standard Integrals
1) $\int{x^n}dx= \frac{x^{n+1}}{n+1}+c $
2) $\int{}dx= x+c$
3) $\int{\sin x }~dx= -\cos {x}+c $
4) $\int{\cos{x}}~dx= \sin{x}+c$
5)$\int{\sec^2 {x}}~dx= \tan{x}+c$
6) $\int{\cosec^2{x}}~dx = - \cot{x}+c $
7) $\int{\sec x ~\tan x}~dx = \sec x +c $
8)$\int{\cosec x ~\cot x}dx= - \cosec x +c$
9)$\int{\tan{x}}~dx= \log(\sec x)+c$
10) $\int{\cot{x}}~dx= \log{(\sin x)}+c$
11) $\int{\frac{1}{x}}dx= \log x +c $
12)$\int {e^x}dx= e^x +c $
13) $\int{a^x}dx= \frac{a^x}{\log a}+c $
Integration of Composite Function
1)$\int {(ax+b)^n}dx= \frac{(ax+b)^{n+1}}{a(n+1)}+c $
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