[britva]

\( \color{red}{\boxed{}} \) Integrales: definidas e indefinidas
\( \color{green}{\boxed{}} \) Ecuaciones diferenciales ordinarias (de diferentes órdenes)
\( \color{blue}{\boxed{}} \) Funciones derivadas
\( \color{brown}{\boxed{}} \) Expresiones matriciales

Enlace:
\( \color{blue}{\rightarrow} \)https://mathdf.com/es/

Ejemplos de:
\( \color{red}{\boxed{}} \)

Spoiler

1) \( \displaystyle\int{\dfrac{1}{\sqrt[{n}]{x}+\sqrt{x}+\tau_{z}+\tau_{11}+\tau_{10}+c_{n}+b_{13}+a_{12}}}{\;\mathrm{d}\tau_{z}}=\ln\left(\tau_{z}+\tau_{11}+\tau_{10}+\sqrt[{n}]{x}+c_{n}+b_{13}+a_{12}+\sqrt{x}\right)+C \)
2) \( \displaystyle\int{\dfrac{x^{4}}{\left(a\,x^{4}+b\right)^{2}}}{\;\mathrm{d}x}=\dfrac{\ln\left(\sqrt{a}\,x^{2}+\sqrt{2}\,\sqrt[{4}]{a}\,\sqrt[{4}]{b}\,x+\sqrt{b}\right)}{16\,\sqrt{2}\,a\,\sqrt[{4}]{a}\,\sqrt[{4}]{b^{3}}}-\dfrac{\ln\left(\sqrt{a}\,x^{2}-\sqrt{2}\,\sqrt[{4}]{a}\,\sqrt[{4}]{b}\,x+\sqrt{b}\right)}{16\,\sqrt{2}\,a\,\sqrt[{4}]{a}\,\sqrt[{4}]{b^{3}}}-\dfrac{\arctan\left(\frac{\sqrt{b}-\sqrt{a}\,x^{2}}{\sqrt{2}\,\sqrt[{4}]{a}\,\sqrt[{4}]{b}\,x}\right)}{8\,\sqrt{2}\,a\,\sqrt[{4}]{a}\,\sqrt[{4}]{b^{3}}}-\dfrac{x}{4\,a\,\left(a\,x^{4}+b\right)}+C \)

https://mathdf.com/int/es/

Colección de integrales resueltas - Google Drive - .pdf

[cerrar]

\( \color{green}{\boxed{}} \)

Spoiler

1) \( \left(x^{2}\,\cot\left(y\right)-3\,\cos\left(y\right)\right)\,\mathrm{d}y+x\,\mathrm{d}x=0\;\rightarrow\;\dfrac{x^{2}\,\sin^{2}\left(y\right)}{2}-\sin^{3}\left(y\right)=C \)

2) \( y\,\mathrm{d}x-x\,\mathrm{d}y=2\,x^{3}\,\tan\left(\frac{y}{x}\right)\,\mathrm{d}x\;\rightarrow\;y=x\,\arcsin\left(C\,e^{x^{2}}\right) \)

https://mathdf.com/dif/es/

[cerrar]

\( \color{blue}{\boxed{}} \)

Spoiler

1) \( \left(z=x\,y\right)'_{x}\;\rightarrow\;z'=x\,y'+y\;{\small\quad y=y\left(x\right),\;z=z\left(x\right)} \)

2) \( \left(x^{x}\,\sin\left(x\right)\right)'_{x}=x^{x}\,\ln\left(x\right)\,\sin\left(x\right)+x^{x}\,\sin\left(x\right)+x^{x}\,\cos\left(x\right) \)

https://mathdf.com/der/es/

[cerrar]

\( \color{brown}{\boxed{}} \)

Spoiler

1) \( \left(\begin{matrix}\alpha&\beta&\sigma\\x&x^{2}&x^{3}\\\sin\left(x\right)&5&3\end{matrix}\right)^{2}=\left(\begin{matrix}\sigma\,\sin\left(x\right)+\beta\,x+\alpha^{2}&\beta\,x^{2}+5\,\sigma+\alpha\,\beta&\beta\,x^{3}+\alpha\,\sigma+3\,\sigma\\x^{3}\,\sin\left(x\right)+x^{3}+\alpha\,x&x^{4}+5\,x^{3}+\beta\,x&x^{5}+3\,x^{3}+\sigma\,x\\\alpha\,\sin\left(x\right)+3\,\sin\left(x\right)+5\,x&\beta\,\sin\left(x\right)+5\,x^{2}+15&\sigma\,\sin\left(x\right)+5\,x^{3}+9\end{matrix}\right) \)

2) \( \displaystyle\int{\left(\begin{matrix}\arcsin\left(x\right)&\operatorname{arsinh}\left(x\right)\\\arccos\left(x\right)&\operatorname{arcosh}\left(x\right)\\\arctan\left(x\right)&\operatorname{artanh}\left(x\right)\\\operatorname{arccot}\left(x\right)&\operatorname{arcoth}\left(x\right)\\\operatorname{arcsec}\left(x\right)&\operatorname{arsech}\left(x\right)\\\operatorname{arccsc}\left(x\right)&\operatorname{arcsch}\left(x\right)\end{matrix}\right)}{\mathrm{d}x}=\left(\begin{matrix}x\,\arcsin\left(x\right)+\sqrt{1-x^{2}}&x\,\operatorname{arsinh}\left(x\right)-\sqrt{x^{2}+1}\\x\,\arccos\left(x\right)-\sqrt{1-x^{2}}&x\,\operatorname{arcosh}\left(x\right)-\sqrt{x^{2}-1}\\x\,\arctan\left(x\right)-\dfrac{\ln\left(x^{2}+1\right)}{2}&\dfrac{\ln\left(1-x^{2}\right)}{2}+x\,\operatorname{artanh}\left(x\right)\\\dfrac{\ln\left(x^{2}+1\right)}{2}+x\,\operatorname{arccot}\left(x\right)&\dfrac{\ln\left(1-x^{2}\right)}{2}+x\,\operatorname{arcoth}\left(x\right)\\x\,\operatorname{arcsec}\left(x\right)-\dfrac{\ln\left(\sqrt{1-\frac{1}{x^{2}}}+1\right)}{2}+\dfrac{\ln\left(1-\sqrt{1-\frac{1}{x^{2}}}\right)}{2}&x\,\operatorname{arsech}\left(x\right)-\arctan\left(\sqrt{\frac{1}{x^{2}}-1}\right)\\x\,\operatorname{arccsc}\left(x\right)+\dfrac{\ln\left(\sqrt{1-\frac{1}{x^{2}}}+1\right)}{2}-\dfrac{\ln\left(1-\sqrt{1-\frac{1}{x^{2}}}\right)}{2}&x\,\operatorname{arcsch}\left(x\right)+\dfrac{\ln\left(\sqrt{\frac{1}{x^{2}}+1}+1\right)}{2}-\dfrac{\ln\left(\sqrt{\frac{1}{x^{2}}+1}-1\right)}{2}\end{matrix}\right) \)
https://mathdf.com/mat/es/

[cerrar]

[Luis Fuentes]

Hola

 No he probado ni mucho menos todos los cálculos que hace, pero tiene muy buena pinta.

Saludos.

[britva]

Calculadora numérica agregada:
https://mathdf.com/calc/es/

La imagen no se visualiza bajo el alerón?