A.4: Tabla de Integrales
- Page ID
- 118877
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)A lo largo de esta tabla,\(a\) y\(b\) se les dan constantes, independientes\(x\) y\(C\) es una constante arbitraria.
| \(f(x)\) | \(F(x)=\int f(x)\ \mathrm{d}{x} \) |
| \(af(x)+bg(x)\) | \(a\int f(x)\ \mathrm{d}{x} +b\int g(x)\ \mathrm{d}{x} \ +\ C\) |
| \(f(x)+g(x)\) | \(\int f(x)\ \mathrm{d}{x} +\int g(x)\ \mathrm{d}{x} \ +\ C\) |
| \(f(x)-g(x)\) | \(\int f(x)\ \mathrm{d}{x} -\int g(x)\ \mathrm{d}{x} \ +\ C\) |
| \(af(x)\) | \(a\int f(x)\ \mathrm{d}{x} \ +\ C\) |
| \(u(x)v'(x)\) | \(u(x)v(x)-\int u'(x)v(x)\ \mathrm{d}{x} \ +\ C\) |
| \(f\big(y(x)\big)y'(x)\) | \(F\big(y(x)\big)\hbox{ where }F(y)=\int f(y)\ \mathrm{d}{y} \) |
| \(a\) | \(ax+C\) |
| \(x^a\) | \(\frac{x^{a+1}}{a+1}+C\hbox{ if }a\ne-1\) |
| \(\frac{1}{x}\) | \(\ln|x|+C\) |
| \(g(x)^ag'(x)\) | \(\frac{g(x)^{a+1}}{a+1}+C\hbox{ if }a\ne -1\) |
| \(f(x)\) | \(F(x)=\int f(x)\ \mathrm{d}{x} \) |
| \(\sin x\) | \(-\cos x+C\) |
| \(g'(x)\sin g(x)\) | \(-\cos g(x)+C\) |
| \(\cos x\) | \(\sin x+C\) |
| \(\tan x\) | \(\ln|\sec x|+C\) |
| \(\csc x\) | \(\ln |\csc x-\cot x|+C\) |
| \(\sec x\) | \(\ln |\sec x+\tan x|+C\) |
| \(\cot x\) | \(\ln|\sin x|+C\) |
| \(\sec^2 x\) | \(\tan x+C\) |
| \(\csc^2 x\) | \(-\cot x+C\) |
| \(\sec x\tan x\) | \(\sec x+C\) |
| \(\csc x\cot x\) | \(-\csc x+C\) |
| \(f(x)\) | \(F(x)=\int f(x)\ \mathrm{d}{x} \) |
| \(e^x\) | \(e^x+C\) |
| \(e^{g(x)}g'(x)\) | \(e^{g(x)}+C\) |
| \(e^{ax}\) | \(\frac{1}{a}\ e^{ax}+C\) |
| \(a^x\) | \(\frac{1}{\ln a}\ a^x+C\) |
| \(\ln x\) | \(x\ln x -x+C\) |
| \(\frac{1}{\sqrt{1-x^2}}\) | \(\arcsin x+C\) |
| \(\frac{g'(x)}{\sqrt{1-g(x)^2}}\) | \(\arcsin g(x)+C\) |
| \(\frac{1}{\sqrt{a^2-x^2}}\) | \(\arcsin \frac{x}{a}+C\) |
| \(\frac{1}{1+x^2}\) | \(\arctan x+C\) |
| \(\frac{g'(x)}{1+g(x)^2}\) | \(\arctan g(x)+C\) |
| \(\frac{1}{a^2+x^2}\) | \(\frac{1}{a}\arctan \frac{x}{a}+C\) |
| \(\frac{1}{x\sqrt{x^2-1}}\) | \(\textrm{arcsec} x+C\)\ quad (\(x \gt 1\)) |