Tabla de integrales

\begin{equation}
\int k \,dx = kx +C
\end{equation}

\begin{equation}
\int x^n \,dx = \frac{1}{n+1}x^{n+1} +C, \hspace{1ex} n\neq-1
\end{equation}

\begin{equation}
\int \frac{1}{x}\,dx = \ln |x|+C
\end{equation}

\begin{equation}
\int e^x \,dx = e^x +C
\end{equation}

\begin{equation}
\int a^x \,dx = \frac{1}{\ln a} a^x+C
\end{equation}

\begin{equation}
\int \sin x \,dx = -\cos x+C
\end{equation}

\begin{equation}
\int \cos x \,dx = \sin x+C
\end{equation}

\begin{equation}
\int \tan x \,dx = \ln |\sec x| +C
\end{equation}

\begin{equation}
\int \ln x \,dx = x \ln x - x+C
\end{equation}

\begin{equation}
\int \sec x \,dx = \ln |\sec x + \tan x|+C
\end{equation}

\begin{equation}
\int \sec^2 x \,dx = \tan x+C
\end{equation}

\begin{equation}
\int \sec x \tan x \,dx = \sec x+C
\end{equation}

\begin{equation}
\int \frac{a}{a^2+x^2}\,dx = \tan^{-1}\frac{x}{a}+C
\end{equation}

\begin{equation}
\int \frac{a}{a^2-x^2}\,dx = \frac{1}{2}\ln\left|\frac{x+a}{x-a}\right|+C
\end{equation}

\begin{equation}
\int \frac{1}{\sqrt{a^2-x^2}} \,dx = \sin^{-1} \frac{x}{a}+C
\end{equation}

\begin{equation}
\int \frac{a}{x \sqrt{x^2-a^2}} \,dx = \sec^{-1} \frac{x}{a}+C
\end{equation}

\begin{align}
\int \frac{1}{\sqrt{x^2-a^2}} \,dx &= \cosh^{-1} \frac{x}{a} \\&= \nonumber \ln (x+\sqrt{x^2-a^2})+C
\end{align}

\begin{align}
\int \frac{1}{\sqrt{x^2+a^2}} \,dx &= \sinh^{-1} \frac{x}{a} \\&=\nonumber \ln (x+\sqrt{x^2+a^2})+C
\end{align}