Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cos(x)*log(3-x)-sin(x)/(3-x)+x/((2+x^2)*sqrt(x^2+1))
¿Cómo vas a descomponer esta cos(x)*log(3-x)-sin(x)/(3-x)+x/((2+x^2)*sqrt(x^2+1)) expresión en fracciones?
Solución
Ha introducido
[src]
sin(x) x
cos(x)*log(3 - x) - ------ + --------------------
3 - x ________
/ 2\ / 2
\2 + x /*\/ x + 1
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \left(\log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}\right)$$
cos(x)*log(3 - x) - sin(x)/(3 - x) + x/(((2 + x^2)*sqrt(x^2 + 1)))
Simplificación general
[src]
sin(x) x
------ + cos(x)*log(3 - x) + --------------------
-3 + x ________
/ 2 / 2\
\/ 1 + x *\2 + x /
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x - 3}$$
sin(x)/(-3 + x) + cos(x)*log(3 - x) + x/(sqrt(1 + x^2)*(2 + x^2))
Respuesta numérica
[src]
cos(x)*log(3 - x) - sin(x)/(3.0 - x) + x*(1.0 + x^2)^(-0.5)/(2.0 + x^2)
cos(x)*log(3 - x) - sin(x)/(3.0 - x) + x*(1.0 + x^2)^(-0.5)/(2.0 + x^2)
Denominador común
[src]
________ ________
2 / 2 2 / 2
x - 3*x + 2*\/ 1 + x *sin(x) + x *\/ 1 + x *sin(x)
--------------------------------------------------------------------- + cos(x)*log(3 - x)
________ ________ ________ ________
/ 2 3 / 2 2 / 2 / 2
- 6*\/ 1 + x + x *\/ 1 + x - 3*x *\/ 1 + x + 2*x*\/ 1 + x
$$\log{\left(3 - x \right)} \cos{\left(x \right)} + \frac{x^{2} \sqrt{x^{2} + 1} \sin{\left(x \right)} + x^{2} - 3 x + 2 \sqrt{x^{2} + 1} \sin{\left(x \right)}}{x^{3} \sqrt{x^{2} + 1} - 3 x^{2} \sqrt{x^{2} + 1} + 2 x \sqrt{x^{2} + 1} - 6 \sqrt{x^{2} + 1}}$$
(x^2 - 3*x + 2*sqrt(1 + x^2)*sin(x) + x^2*sqrt(1 + x^2)*sin(x))/(-6*sqrt(1 + x^2) + x^3*sqrt(1 + x^2) - 3*x^2*sqrt(1 + x^2) + 2*x*sqrt(1 + x^2)) + cos(x)*log(3 - x)
Denominador racional
[src]
________ ________ ________ ________ ________ ________
2 / 2 2 / 2 / 2 3 / 2 2 / 2 / 2
x - 3*x + 2*\/ 1 + x *sin(x) + x *\/ 1 + x *sin(x) - 6*\/ 1 + x *cos(x)*log(3 - x) + x *\/ 1 + x *cos(x)*log(3 - x) - 3*x *\/ 1 + x *cos(x)*log(3 - x) + 2*x*\/ 1 + x *cos(x)*log(3 - x)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
________
/ 2 / 2\
\/ 1 + x *(-3 + x)*\2 + x /
$$\frac{x^{3} \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} - 3 x^{2} \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} + x^{2} \sqrt{x^{2} + 1} \sin{\left(x \right)} + x^{2} + 2 x \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} - 3 x - 6 \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} + 2 \sqrt{x^{2} + 1} \sin{\left(x \right)}}{\left(x - 3\right) \sqrt{x^{2} + 1} \left(x^{2} + 2\right)}$$
(x^2 - 3*x + 2*sqrt(1 + x^2)*sin(x) + x^2*sqrt(1 + x^2)*sin(x) - 6*sqrt(1 + x^2)*cos(x)*log(3 - x) + x^3*sqrt(1 + x^2)*cos(x)*log(3 - x) - 3*x^2*sqrt(1 + x^2)*cos(x)*log(3 - x) + 2*x*sqrt(1 + x^2)*cos(x)*log(3 - x))/(sqrt(1 + x^2)*(-3 + x)*(2 + x^2))
Potencias
[src]
/ I*x -I*x\ / -I*x I*x\
|e e | x I*\- e + e /
|---- + -----|*log(3 - x) + -------------------- + ------------------
\ 2 2 / ________ 2*(3 - x)
/ 2 / 2\
\/ 1 + x *\2 + x /
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \log{\left(3 - x \right)} + \frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(3 - x\right)}$$
sin(x) x
cos(x)*log(3 - x) - ------ + --------------------
3 - x ________
/ 2 / 2\
\/ 1 + x *\2 + x /
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$
cos(x)*log(3 - x) - sin(x)/(3 - x) + x/(sqrt(1 + x^2)*(2 + x^2))
Combinatoria
[src]
________ ________ ________ ________ ________ ________
2 / 2 2 / 2 / 2 3 / 2 2 / 2 / 2
x - 3*x + 2*\/ 1 + x *sin(x) + x *\/ 1 + x *sin(x) - 6*\/ 1 + x *cos(x)*log(3 - x) + x *\/ 1 + x *cos(x)*log(3 - x) - 3*x *\/ 1 + x *cos(x)*log(3 - x) + 2*x*\/ 1 + x *cos(x)*log(3 - x)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
________
/ 2 / 2\
\/ 1 + x *(-3 + x)*\2 + x /
$$\frac{x^{3} \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} - 3 x^{2} \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} + x^{2} \sqrt{x^{2} + 1} \sin{\left(x \right)} + x^{2} + 2 x \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} - 3 x - 6 \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} + 2 \sqrt{x^{2} + 1} \sin{\left(x \right)}}{\left(x - 3\right) \sqrt{x^{2} + 1} \left(x^{2} + 2\right)}$$
(x^2 - 3*x + 2*sqrt(1 + x^2)*sin(x) + x^2*sqrt(1 + x^2)*sin(x) - 6*sqrt(1 + x^2)*cos(x)*log(3 - x) + x^3*sqrt(1 + x^2)*cos(x)*log(3 - x) - 3*x^2*sqrt(1 + x^2)*cos(x)*log(3 - x) + 2*x*sqrt(1 + x^2)*cos(x)*log(3 - x))/(sqrt(1 + x^2)*(-3 + x)*(2 + x^2))
Compilar la expresión
[src]
sin(x) x
cos(x)*log(3 - x) - ------ + --------------------
3 - x ________
/ 2 / 2\
\/ 1 + x *\2 + x /
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$
cos(x)*log(3 - x) - sin(x)/(3 - x) + x/(sqrt(1 + x^2)*(2 + x^2))
Unión de expresiones racionales
[src]
________
/ 2 / 2\
x*(3 - x) + \/ 1 + x *\2 + x /*(-sin(x) + (3 - x)*cos(x)*log(3 - x))
----------------------------------------------------------------------
________
/ 2 / 2\
\/ 1 + x *\2 + x /*(3 - x)
$$\frac{x \left(3 - x\right) + \sqrt{x^{2} + 1} \left(x^{2} + 2\right) \left(\left(3 - x\right) \log{\left(3 - x \right)} \cos{\left(x \right)} - \sin{\left(x \right)}\right)}{\left(3 - x\right) \sqrt{x^{2} + 1} \left(x^{2} + 2\right)}$$
(x*(3 - x) + sqrt(1 + x^2)*(2 + x^2)*(-sin(x) + (3 - x)*cos(x)*log(3 - x)))/(sqrt(1 + x^2)*(2 + x^2)*(3 - x))
Parte trigonométrica
[src]
/ pi\ sin(x) x
log(3 - x)*sin|x + --| - ------ + --------------------
\ 2 / 3 - x ________
/ 2 / 2\
\/ 1 + x *\2 + x /
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \sin{\left(x + \frac{\pi}{2} \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$
log(3 - x) 1 x
---------- - -------------- + --------------------
sec(x) (3 - x)*csc(x) ________
/ 2 / 2\
\/ 1 + x *\2 + x /
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \frac{\log{\left(3 - x \right)}}{\sec{\left(x \right)}} - \frac{1}{\left(3 - x\right) \csc{\left(x \right)}}$$
/ 2/x\\ /x\
|-1 + cot |-||*log(3 - x) 2*cot|-|
x \ \2// \2/
-------------------- + ------------------------- - ---------------------
________ 2/x\ / 2/x\\
/ 2 / 2\ 1 + cot |-| |1 + cot |-||*(3 - x)
\/ 1 + x *\2 + x / \2/ \ \2//
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \log{\left(3 - x \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \cot{\left(\frac{x}{2} \right)}}{\left(3 - x\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/ 2/x\\ /x\
|1 - tan |-||*log(3 - x) 2*tan|-|
x \ \2// \2/
-------------------- + ------------------------ - ---------------------
________ 2/x\ / 2/x\\
/ 2 / 2\ 1 + tan |-| |1 + tan |-||*(3 - x)
\/ 1 + x *\2 + x / \2/ \ \2//
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \log{\left(3 - x \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\left(3 - x\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
x sin(x)
-------------------- + cos(x)*log(3 - x) - ------
________ 3 - x
/ 2\ / 2
\2 + x /*\/ x + 1
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$
/ pi\
cos|x - --|
\ 2 / x
cos(x)*log(3 - x) - ----------- + --------------------
3 - x ________
/ 2 / 2\
\/ 1 + x *\2 + x /
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{3 - x}$$
log(3 - x) 1 x ----------- - -------------- + -------------------- /pi \ (3 - x)*csc(x) ________ csc|-- - x| / 2 / 2\ \2 / \/ 1 + x *\2 + x /
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \frac{\log{\left(3 - x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{1}{\left(3 - x\right) \csc{\left(x \right)}}$$
sin(x) x
cos(x)*log(3 - x) - ------ + --------------------
3 - x ________
/ 2 / 2\
\/ 1 + x *\2 + x /
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$
log(3 - x) 1 x
---------- - ------------------- + --------------------
sec(x) / pi\ ________
(3 - x)*sec|x - --| / 2 / 2\
\ 2 / \/ 1 + x *\2 + x /
$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \frac{\log{\left(3 - x \right)}}{\sec{\left(x \right)}} - \frac{1}{\left(3 - x\right) \sec{\left(x - \frac{\pi}{2} \right)}}$$
log(3 - x)/sec(x) - 1/((3 - x)*sec(x - pi/2)) + x/(sqrt(1 + x^2)*(2 + x^2))