Tabla de Integrales Indefinidas

Referencia: Leon W Couch Apéndice p656

Integrales Indefinidas

$\int (a+bx)^n dx = \frac{(a+bx)^{n+1}} {b(n+1)}, 0<n$ $\int \frac{dx}{a+bx} =\frac{1}{b} ln|a+bx|$ $\int \frac{dx}{(a+bx)^n} = \frac{-1}{(n-1)b(a+bx)^{n-1}} , 1<n$

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$\int \frac{dx}{(c+bc+ax^2)^n} =$ $= \begin{cases} \frac{2}{ \sqrt{4ac-b^2}} tan^{-1}\left(\frac{2ax+b}{\sqrt{4ac-b^2}}\right) , & b^{2} < 4ac \\ \frac{1}{\sqrt{b^2-4ac}}ln\left| \frac{2ax+b-\sqrt{b^2-4ac}}{2ax+b+\sqrt{b^2-4ac}} \right| , & b^{2} > 4ac \\ \frac{-2}{\sqrt{2ax+b}} , & b^{2}=4ac \end{cases}$

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$\int \frac{x dx}{c+bx+ax^2} =$ $= \frac{1}{2a} ln\left| ax^2+bx+c \right| - \frac{b}{2a}\int \frac{dx}{c+bx+ax^2}$

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$\int \frac{dx}{a^2+b^2x^2} = \frac{1}{ab} tan^{-1}\left( \frac{bx}{a} \right)$ $\int \frac{x dx}{a^2+x^2} = \frac{1}{2} ln( a^2+x^2 )$

Trigonométricas

$\int cos(x) dx = sen(x)$ $\int sen(x) dx = -cos(x)$ $\int x cos(x) dx = cos(x) + x sen(x)$ $\int x sen(x) dx = sen(x) - x cos(x)$ $\int x^2 cos(x) dx = 2x cos(x) + (x^2 -2) sen(x)$ $\int x^2 sen(x) dx = 2x sen(x) - (x^2 -2) cos(x)$

Exponenciales

$\int e^{ax} dx = \frac{e^{ax}}{a}$ $\int x e^{ax} dx = e^{ax} \left( \frac{x}{a} - \frac{1}{a^2} \right)$ $\int x^2 e^{ax} dx = e^{ax} \left( \frac{x^2}{a} - \frac{2x}{a^2} + \frac{2}{a^3} \right)$ $\int x^3 e^{ax} dx = e^{ax} \left( \frac{x^3}{a} - \frac{3x^2}{a^2} + \frac{6x}{a^3} - \frac{6}{a^4}\right)$ $\int e^{ax} sen(x) dx = \frac{e^{ax}}{a^2 +1} (a sen(x) - cos(x))$ $\int e^{ax} cos(x) dx = \frac{e^{ax}}{a^2 +1} (a cos(x) - sen(x))$