math formulas

\large sin^2\alpha + cos^2\alpha = 1

\large tan\alpha = \frac{1}{cot\alpha}

\large tan^2\alpha + 1 = \frac{1}{cos^2\alpha}

\large cot^2\alpha + 1 = \frac{1}{sin^2\alpha}

\large \lim_{x\to0}\frac{sinx}{x} = 1

\large \lim_{x\to0}(1+x)^{\frac{1}{x}} = e

\large f'(x) = \lim_{\Delta x\to0}\frac{f(x+\Delta x) - f(x)}{\Delta x}

\large (f \pm g)' = f' \pm g'

\large (uv)' = u'v + v'u

\large (\frac{u}{v})' = \frac{u'v - v'u}{v^2}

\large u(v(x))'_x = u(v)'_v v(x)'_x

\large \int f(x)dx = F(x) + C

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

\large \int_a^bf(x)dx = F(b) - F(a)

\large \int_a^bf(x)dx = -\int_b^af(x)dx

\large \int_a^bf(x)dx = \int_a^cf(x)dx + \int_c^bf(x)dx

\large \int d(F(x)) = F(x) + C

\large d(\int F(x)) = F(x)

\large \int udv = uv - \int vdu

\large \frac{1}{1-x} = \sum_{n=0}^\infty x^n

\large e^x = \sum_{n=0}^\infty \frac{x^n}{n!}

\large sin(x) = \sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)!}

\large cos(x) = \sum_{n=0}^\infty\frac{(-1)^nx^{2n}}{(2n)!}

\large log(1+x) = \sum_{n=1}^{\infty}\frac{(-1)^{n+1}x^n}{n}

some math formulas