Integrals

\displaystyle \int^{b}_{a} f(x) dx = F(x) \bigm|^{a}_{b}

\displaystyle \int k dx = 0

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

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

\displaystyle \int f(x) \pm g(x) dx = \int f(x) dx \pm \int g(x) dx

USEFUL INTEGRALS

\displaystyle \int k dx = kx+c

\displaystyle \int x^{n} dx = \frac{1}{n+1} x^{n+1}+c

\displaystyle \int \frac{1}{x} dx = ln \left| x \right|+c

\displaystyle \int ln(x) dx = xln(x)-x+c

\displaystyle \int e^{x} dx = e^{x}+c

\displaystyle \int cos(x) dx = sin(x)+c

\displaystyle \int sin(x) dx = -cos(x)+c

\displaystyle \int tan(x) dx = ln \left( \left| sec(x) \right| \right)+c

\displaystyle \int \frac{1}{a^{2}+u^{2}} dx = \frac{1}{a} tan^{-1} \left( \frac{u}{a} \right)+c

\displaystyle \int \frac{1}{a^{2}-u^{2}} dx = sin^{-1} \left( \frac{u}{a} \right)+c