Sr Examen
¿Cómo vas a descomponer esta ln(1/(2x))^tgx expresión en fracciones?
Solución
Ha introducido
[src]
tan(x)/ 1 \
log |---|
\2*x/
$$\log{\left(\frac{1}{2 x} \right)}^{\tan{\left(x \right)}}$$
log(1/(2*x))^tan(x)
Descomposición de una fracción
[src]
(-log(2) + log(1/x))^tan(x)
$$\left(\log{\left(\frac{1}{x} \right)} - \log{\left(2 \right)}\right)^{\tan{\left(x \right)}}$$
tan(x) / /1\\ |-log(2) + log|-|| \ \x//
Potencias
[src]
/ I*x -I*x\
I*\- e + e /
------------------
I*x -I*x
e + e
/ / 1 \\
|log|---||
\ \2*x//
$$\log{\left(\frac{1}{2 x} \right)}^{\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}}}$$
log(1/(2*x))^(i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))
Combinatoria
[src]
tan(x) / /1\\ |-log(2) + log|-|| \ \x//
$$\left(\log{\left(\frac{1}{x} \right)} - \log{\left(2 \right)}\right)^{\tan{\left(x \right)}}$$
(-log(2) + log(1/x))^tan(x)
Denominador común
[src]
tan(x) / /1\\ |-log(2) + log|-|| \ \x//
$$\left(\log{\left(\frac{1}{x} \right)} - \log{\left(2 \right)}\right)^{\tan{\left(x \right)}}$$
(-log(2) + log(1/x))^tan(x)
Parte trigonométrica
[src]
/ pi\
cos|x - --|
\ 2 /
-----------
cos(x)
/ / 1 \\
|log|---||
\ \2*x//
$$\log{\left(\frac{1}{2 x} \right)}^{\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}}$$
sin(x)
------
cos(x)
/ / 1 \\
|log|---||
\ \2*x//
$$\log{\left(\frac{1}{2 x} \right)}^{\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}}$$
sec(x)
------
csc(x)
/ / 1 \\
|log|---||
\ \2*x//
$$\log{\left(\frac{1}{2 x} \right)}^{\frac{\sec{\left(x \right)}}{\csc{\left(x \right)}}}$$
1
------
cot(x)
/ / 1 \\
|log|---||
\ \2*x//
$$\log{\left(\frac{1}{2 x} \right)}^{\frac{1}{\cot{\left(x \right)}}}$$
2
2*sin (x)
---------
sin(2*x)
/ / 1 \\
|log|---||
\ \2*x//
$$\log{\left(\frac{1}{2 x} \right)}^{\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}}$$
sec(x)
-----------
/ pi\
sec|x - --|
\ 2 /
/ / 1 \\
|log|---||
\ \2*x//
$$\log{\left(\frac{1}{2 x} \right)}^{\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}}$$
/pi \
csc|-- - x|
\2 /
-----------
csc(x)
/ / 1 \\
|log|---||
\ \2*x//
$$\log{\left(\frac{1}{2 x} \right)}^{\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}}$$
log(1/(2*x))^(csc(pi/2 - x)/csc(x))