Integrali fondamentali

Alcuni degli integrali immediati sono:

• $\int adx=ax+c$

• $\int x^{a}dx=\frac{x^{a+1}}{a+1}+c$

• $\int \frac{1}{x}dx=\ln |x|+c$

• $\int e^{x}dx=e^x+c$

• $\int \sin (x)dx=-\cos (x)+c$

• $\int \cos (x)dx=\sin (x)+c$

• $\int \frac{1}{1+x^2}dx=\arctan (x)+c$

Mentre quelli generalizzati:

• $\int (f(x){)}^a{f}^{\prime }(x)dx=\frac{(f(x){)}^{a+1}}{a+1}+c$

• $\int \frac{f^{\prime }(x)}{f(x)}dx=\ln |f(x)|+c$

• $\int f^{\prime }(x)e^{f(x)}dx=e^{f(x)}+c$

• $\int f^{\prime }(x)\sin (f(x))dx=-\cos (f(x))+c$

• $\int f^{\prime }(x)\cos (f(x))dx=\sin (f(x))+c$

• $\int \frac{f^{\prime }(x)}{1+f^2(x)}dx=\arctan (f(x))+c$