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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(x)^(sqrt(x))*(log(tan(x))/(2*sqrt(x))+sqrt(x)*(1+tan(x)^2)/tan(x))

¿Cómo vas a descomponer esta tan(x)^(sqrt(x))*(log(tan(x))/(2*sqrt(x))+sqrt(x)*(1+tan(x)^2)/tan(x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
          ___ /                ___ /       2   \\
        \/ x  |log(tan(x))   \/ x *\1 + tan (x)/|
(tan(x))     *|----------- + -------------------|
              |      ___            tan(x)      |
              \  2*\/ x                         /
(x(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x))2x)tan⁡x(x)\left(\frac{\sqrt{x} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \tan^{\sqrt{x}}{\left(x \right)} 
tan(x)^(sqrt(x))*(log(tan(x))/((2*sqrt(x))) + (sqrt(x)*(1 + tan(x)^2))/tan(x))
Simplificación general [src] 
               ___                               
        -1 + \/ x  /   x      log(tan(x))*tan(x)\
(tan(x))          *|------- + ------------------|
                   |   2              2         |
                   \cos (x)                     /
-------------------------------------------------
                        ___                      
                      \/ x
(xcos⁡2(x)+log⁡(tan⁡(x))tan⁡(x)2)tan⁡x−1(x)x\frac{\left(\frac{x}{\cos^{2}{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}}{2}\right) \tan^{\sqrt{x} - 1}{\left(x \right)}}{\sqrt{x}} 
tan(x)^(-1 + sqrt(x))*(x/cos(x)^2 + log(tan(x))*tan(x)/2)/sqrt(x)
Respuesta numérica [src] 
tan(x)^(x^0.5)*(0.5*x^(-0.5)*log(tan(x)) + x^0.5*(1.0 + tan(x)^2)/tan(x))
tan(x)^(x^0.5)*(0.5*x^(-0.5)*log(tan(x)) + x^0.5*(1.0 + tan(x)^2)/tan(x))
Denominador común [src] 
              ___             ___                                            ___
            \/ x            \/ x                              2            \/ x 
2*x*(tan(x))      + (tan(x))     *log(tan(x))*tan(x) + 2*x*tan (x)*(tan(x))     
--------------------------------------------------------------------------------
                                     ___                                        
                                 2*\/ x *tan(x)
2xtan⁡2(x)tan⁡x(x)+2xtan⁡x(x)+log⁡(tan⁡(x))tan⁡(x)tan⁡x(x)2xtan⁡(x)\frac{2 x \tan^{2}{\left(x \right)} \tan^{\sqrt{x}}{\left(x \right)} + 2 x \tan^{\sqrt{x}}{\left(x \right)} + \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)} \tan^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x} \tan{\left(x \right)}} 
(2*x*tan(x)^(sqrt(x)) + tan(x)^(sqrt(x))*log(tan(x))*tan(x) + 2*x*tan(x)^2*tan(x)^(sqrt(x)))/(2*sqrt(x)*tan(x))
Combinatoria [src] 
          ___                                         
        \/ x  /                                  2   \
(tan(x))     *\2*x + log(tan(x))*tan(x) + 2*x*tan (x)/
------------------------------------------------------
                        ___                           
                    2*\/ x *tan(x)
(2xtan⁡2(x)+2x+log⁡(tan⁡(x))tan⁡(x))tan⁡x(x)2xtan⁡(x)\frac{\left(2 x \tan^{2}{\left(x \right)} + 2 x + \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}\right) \tan^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x} \tan{\left(x \right)}} 
tan(x)^(sqrt(x))*(2*x + log(tan(x))*tan(x) + 2*x*tan(x)^2)/(2*sqrt(x)*tan(x))
Denominador racional [src] 
                   ___                  ___                                                 ___
            -1 + \/ x            -1 + \/ x                              2            -1 + \/ x 
2*x*(tan(x))           + (tan(x))          *log(tan(x))*tan(x) + 2*x*tan (x)*(tan(x))          
-----------------------------------------------------------------------------------------------
                                                ___                                            
                                            2*\/ x
2xtan⁡2(x)tan⁡x−1(x)+2xtan⁡x−1(x)+log⁡(tan⁡(x))tan⁡(x)tan⁡x−1(x)2x\frac{2 x \tan^{2}{\left(x \right)} \tan^{\sqrt{x} - 1}{\left(x \right)} + 2 x \tan^{\sqrt{x} - 1}{\left(x \right)} + \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)} \tan^{\sqrt{x} - 1}{\left(x \right)}}{2 \sqrt{x}} 
(2*x*tan(x)^(-1 + sqrt(x)) + tan(x)^(-1 + sqrt(x))*log(tan(x))*tan(x) + 2*x*tan(x)^2*tan(x)^(-1 + sqrt(x)))/(2*sqrt(x))
Potencias [src] 
                          /                                  /                    2\               \
                          |                                  |    /   I*x    -I*x\ |               |
                          |   /  /   I*x    -I*x\\       ___ |    \- e    + e    / | / I*x    -I*x\|
                      ___ |   |I*\- e    + e    /|   I*\/ x *|1 - -----------------|*\e    + e    /|
                    \/ x  |log|------------------|           |                   2 |               |
/  /   I*x    -I*x\\      |   |    I*x    -I*x   |           |     / I*x    -I*x\  |               |
|I*\- e    + e    /|      |   \   e    + e       /           \     \e    + e    /  /               |
|------------------|     *|----------------------- - ----------------------------------------------|
|    I*x    -I*x   |      |            ___                              I*x    -I*x                |
\   e    + e       /      \        2*\/ x                            - e    + e                    /
(i(−eix+e−ix)eix+e−ix)x(−ix(−(−eix+e−ix)2(eix+e−ix)2+1)(eix+e−ix)−eix+e−ix+log⁡(i(−eix+e−ix)eix+e−ix)2x)\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}}\right)^{\sqrt{x}} \left(- \frac{i \sqrt{x} \left(- \frac{\left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + 1\right) \left(e^{i x} + e^{- i x}\right)}{- e^{i x} + e^{- i x}} + \frac{\log{\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} \right)}}{2 \sqrt{x}}\right) 
(i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))^(sqrt(x))*(log(i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))/(2*sqrt(x)) - i*sqrt(x)*(1 - (-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)*(exp(i*x) + exp(-i*x))/(-exp(i*x) + exp(-i*x)))
Unión de expresiones racionales [src] 
          ___                                         
        \/ x  /                         /       2   \\
(tan(x))     *\log(tan(x))*tan(x) + 2*x*\1 + tan (x)//
------------------------------------------------------
                        ___                           
                    2*\/ x *tan(x)
(2x(tan⁡2(x)+1)+log⁡(tan⁡(x))tan⁡(x))tan⁡x(x)2xtan⁡(x)\frac{\left(2 x \left(\tan^{2}{\left(x \right)} + 1\right) + \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}\right) \tan^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x} \tan{\left(x \right)}} 
tan(x)^(sqrt(x))*(log(tan(x))*tan(x) + 2*x*(1 + tan(x)^2))/(2*sqrt(x)*tan(x))
Abrimos la expresión [src] 
                ___                                          ___            
  ___         \/ x                    ___                  \/ x             
\/ x *(tan(x))          ___         \/ x           (tan(x))     *log(tan(x))
------------------- + \/ x *(tan(x))     *tan(x) + -------------------------
       tan(x)                                                   ___         
                                                            2*\/ x
xtan⁡(x)tan⁡x(x)+xtan⁡x(x)tan⁡(x)+log⁡(tan⁡(x))tan⁡x(x)2x\sqrt{x} \tan{\left(x \right)} \tan^{\sqrt{x}}{\left(x \right)} + \frac{\sqrt{x} \tan^{\sqrt{x}}{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)} \tan^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x}} 
sqrt(x)*tan(x)^(sqrt(x))/tan(x) + sqrt(x)*tan(x)^(sqrt(x))*tan(x) + tan(x)^(sqrt(x))*log(tan(x))/(2*sqrt(x))
Parte trigonométrica [src] 
          ___                                 
        \/ x  /log(tan(x))       ___         \
(tan(x))     *|----------- + 2*\/ x *csc(2*x)|
              |      ___                     |
              \  2*\/ x                      /
(2xcsc⁡(2x)+log⁡(tan⁡(x))2x)tan⁡x(x)\left(2 \sqrt{x} \csc{\left(2 x \right)} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \tan^{\sqrt{x}}{\left(x \right)} 
          ___ /   /  1   \                             \
        \/ x  |log|------|                             |
/  1   \      |   \cot(x)/     ___ /       1   \       |
|------|     *|----------- + \/ x *|1 + -------|*cot(x)|
\cot(x)/      |      ___           |       2   |       |
              \  2*\/ x            \    cot (x)/       /
(x(1+1cot⁡2(x))cot⁡(x)+log⁡(1cot⁡(x))2x)(1cot⁡(x))x\left(\sqrt{x} \left(1 + \frac{1}{\cot^{2}{\left(x \right)}}\right) \cot{\left(x \right)} + \frac{\log{\left(\frac{1}{\cot{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\cot{\left(x \right)}}\right)^{\sqrt{x}} 
                   /                         /         2      \            \
                   |   /   sec(x)  \     ___ |      sec (x)   |    /    pi\|
                   |log|-----------|   \/ x *|1 + ------------|*sec|x - --||
               ___ |   |   /    pi\|         |       2/    pi\|    \    2 /|
             \/ x  |   |sec|x - --||         |    sec |x - --||            |
/   sec(x)  \      |   \   \    2 //         \        \    2 //            |
|-----------|     *|---------------- + ------------------------------------|
|   /    pi\|      |        ___                       sec(x)               |
|sec|x - --||      \    2*\/ x                                             /
\   \    2 //
(sec⁡(x)sec⁡(x−π2))x(x(sec⁡2(x)sec⁡2(x−π2)+1)sec⁡(x−π2)sec⁡(x)+log⁡(sec⁡(x)sec⁡(x−π2))2x)\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(\frac{\sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}} + \frac{\log{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{2 \sqrt{x}}\right) 
          ___ /   /  1   \                      \
        \/ x  |log|------|     ___ /       2   \|
/  1   \      |   \cot(x)/   \/ x *\1 + cot (x)/|
|------|     *|----------- + -------------------|
\cot(x)/      |      ___            cot(x)      |
              \  2*\/ x                         /
(x(cot⁡2(x)+1)cot⁡(x)+log⁡(1cot⁡(x))2x)(1cot⁡(x))x\left(\frac{\sqrt{x} \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} + \frac{\log{\left(\frac{1}{\cot{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\cot{\left(x \right)}}\right)^{\sqrt{x}} 
             ___ /   /     2   \           \
           \/ x  |   |2*sin (x)|           |
/     2   \      |log|---------|       ___ |
|2*sin (x)|      |   \ sin(2*x)/   2*\/ x  |
|---------|     *|-------------- + --------|
\ sin(2*x)/      |       ___       sin(2*x)|
                 \   2*\/ x                /
(2sin⁡2(x)sin⁡(2x))x(2xsin⁡(2x)+log⁡(2sin⁡2(x)sin⁡(2x))2x)\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right)^{\sqrt{x}} \left(\frac{2 \sqrt{x}}{\sin{\left(2 x \right)}} + \frac{\log{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} \right)}}{2 \sqrt{x}}\right) 
                 /                       /         4   \         \
             ___ |   /     2   \     ___ |    4*sin (x)|         |
           \/ x  |   |2*sin (x)|   \/ x *|1 + ---------|*sin(2*x)|
/     2   \      |log|---------|         |       2     |         |
|2*sin (x)|      |   \ sin(2*x)/         \    sin (2*x)/         |
|---------|     *|-------------- + ------------------------------|
\ sin(2*x)/      |       ___                      2              |
                 \   2*\/ x                  2*sin (x)           /
(2sin⁡2(x)sin⁡(2x))x(x(4sin⁡4(x)sin⁡2(2x)+1)sin⁡(2x)2sin⁡2(x)+log⁡(2sin⁡2(x)sin⁡(2x))2x)\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(\frac{4 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}} + \frac{\log{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} \right)}}{2 \sqrt{x}}\right) 
               ___ /   /   /pi    \\                   \
             \/ x  |   |csc|-- - x||                   |
/   /pi    \\      |   |   \2     /|                   |
|csc|-- - x||      |log|-----------|                   |
|   \2     /|      |   \   csc(x)  /       ___         |
|-----------|     *|---------------- + 2*\/ x *csc(2*x)|
\   csc(x)  /      |        ___                        |
                   \    2*\/ x                         /
(csc⁡(−x+π2)csc⁡(x))x(2xcsc⁡(2x)+log⁡(csc⁡(−x+π2)csc⁡(x))2x)\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)^{\sqrt{x}} \left(2 \sqrt{x} \csc{\left(2 x \right)} + \frac{\log{\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) 
                   /                         /       2/    pi\\       \
               ___ |   /   /    pi\\         |    cos |x - --||       |
             \/ x  |   |cos|x - --||     ___ |        \    2 /|       |
/   /    pi\\      |   |   \    2 /|   \/ x *|1 + ------------|*cos(x)|
|cos|x - --||      |log|-----------|         |         2      |       |
|   \    2 /|      |   \   cos(x)  /         \      cos (x)   /       |
|-----------|     *|---------------- + -------------------------------|
\   cos(x)  /      |        ___                     /    pi\          |
                   |    2*\/ x                   cos|x - --|          |
                   \                                \    2 /          /
(cos⁡(x−π2)cos⁡(x))x(x(1+cos⁡2(x−π2)cos⁡2(x))cos⁡(x)cos⁡(x−π2)+log⁡(cos⁡(x−π2)cos⁡(x))2x)\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(1 + \frac{\cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + \frac{\log{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) 
          ___ /                  ___ \
        \/ x  |log(tan(x))   2*\/ x  |
(tan(x))     *|----------- + --------|
              |      ___     sin(2*x)|
              \  2*\/ x              /
(2xsin⁡(2x)+log⁡(tan⁡(x))2x)tan⁡x(x)\left(\frac{2 \sqrt{x}}{\sin{\left(2 x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \tan^{\sqrt{x}}{\left(x \right)} 
              /                    /       2   \       \
              |                ___ |    sin (x)|       |
          ___ |   /sin(x)\   \/ x *|1 + -------|*cos(x)|
        \/ x  |log|------|         |       2   |       |
/sin(x)\      |   \cos(x)/         \    cos (x)/       |
|------|     *|----------- + --------------------------|
\cos(x)/      |      ___               sin(x)          |
              \  2*\/ x                                /
(sin⁡(x)cos⁡(x))x(x(sin⁡2(x)cos⁡2(x)+1)cos⁡(x)sin⁡(x)+log⁡(sin⁡(x)cos⁡(x))2x)\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) 
               ___ /   /   /    pi\\                \
             \/ x  |   |cos|x - --||                |
/   /    pi\\      |   |   \    2 /|                |
|cos|x - --||      |log|-----------|          ___   |
|   \    2 /|      |   \   cos(x)  /      2*\/ x    |
|-----------|     *|---------------- + -------------|
\   cos(x)  /      |        ___           /      pi\|
                   |    2*\/ x         cos|2*x - --||
                   \                      \      2 //
(cos⁡(x−π2)cos⁡(x))x(2xcos⁡(2x−π2)+log⁡(cos⁡(x−π2)cos⁡(x))2x)\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)^{\sqrt{x}} \left(\frac{2 \sqrt{x}}{\cos{\left(2 x - \frac{\pi}{2} \right)}} + \frac{\log{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) 
              /                    /       2   \       \
              |                ___ |    sec (x)|       |
          ___ |   /sec(x)\   \/ x *|1 + -------|*csc(x)|
        \/ x  |log|------|         |       2   |       |
/sec(x)\      |   \csc(x)/         \    csc (x)/       |
|------|     *|----------- + --------------------------|
\csc(x)/      |      ___               sec(x)          |
              \  2*\/ x                                /
(sec⁡(x)csc⁡(x))x(x(1+sec⁡2(x)csc⁡2(x))csc⁡(x)sec⁡(x)+log⁡(sec⁡(x)csc⁡(x))2x)\left(\frac{\sec{\left(x \right)}}{\csc{\left(x \right)}}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(1 + \frac{\sec^{2}{\left(x \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)}}{\sec{\left(x \right)}} + \frac{\log{\left(\frac{\sec{\left(x \right)}}{\csc{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) 
                   /   /   sec(x)  \                        \
                   |log|-----------|                        |
               ___ |   |   /    pi\|                        |
             \/ x  |   |sec|x - --||                        |
/   sec(x)  \      |   \   \    2 //       ___    /      pi\|
|-----------|     *|---------------- + 2*\/ x *sec|2*x - --||
|   /    pi\|      |        ___                   \      2 /|
|sec|x - --||      \    2*\/ x                              /
\   \    2 //
(sec⁡(x)sec⁡(x−π2))x(2xsec⁡(2x−π2)+log⁡(sec⁡(x)sec⁡(x−π2))2x)\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{\sqrt{x}} \left(2 \sqrt{x} \sec{\left(2 x - \frac{\pi}{2} \right)} + \frac{\log{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{2 \sqrt{x}}\right) 
                   /                         /       2/pi    \\       \
               ___ |   /   /pi    \\         |    csc |-- - x||       |
             \/ x  |   |csc|-- - x||     ___ |        \2     /|       |
/   /pi    \\      |   |   \2     /|   \/ x *|1 + ------------|*csc(x)|
|csc|-- - x||      |log|-----------|         |         2      |       |
|   \2     /|      |   \   csc(x)  /         \      csc (x)   /       |
|-----------|     *|---------------- + -------------------------------|
\   csc(x)  /      |        ___                     /pi    \          |
                   |    2*\/ x                   csc|-- - x|          |
                   \                                \2     /          /
(csc⁡(−x+π2)csc⁡(x))x(x(1+csc⁡2(−x+π2)csc⁡2(x))csc⁡(x)csc⁡(−x+π2)+log⁡(csc⁡(−x+π2)csc⁡(x))2x)\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(1 + \frac{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{\log{\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) 
(csc(pi/2 - x)/csc(x))^(sqrt(x))*(log(csc(pi/2 - x)/csc(x))/(2*sqrt(x)) + sqrt(x)*(1 + csc(pi/2 - x)^2/csc(x)^2)*csc(x)/csc(pi/2 - x))
    © Sr Examen – Калькулятор