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log(x^4-x^2+5)/4-atan((2*x^2-1)/sqrt(19))/(2*sqrt(19))
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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^4-x^2+5)/4+atan((2*x^2-1)/sqrt(19))/(2*sqrt(19))

¿Cómo vas a descomponer esta log(x^4-x^2+5)/4+atan((2x^2-1)/sqrt(19))/(2sqrt(19)) expresión en fracciones?

Solución

Ha introducido [src]

                       /   2    \
                       |2*x  - 1|
                   atan|--------|
   / 4    2    \       |   ____ |
log\x  - x  + 5/       \ \/ 19  /
---------------- + --------------
       4                  ____   
                      2*\/ 19

$$\frac{\log{\left(\left(x^{4} - x^{2}\right) + 5 \right)}}{4} + \frac{\operatorname{atan}{\left(\frac{2 x^{2} - 1}{\sqrt{19}} \right)}}{2 \sqrt{19}}$$

log(x^4 - x^2 + 5)/4 + atan((2*x^2 - 1)/sqrt(19))/((2*sqrt(19)))

Simplificación general [src]

                              /  ____ /        2\\
                     ____     |\/ 19 *\-1 + 2*x /|
   /     4    2\   \/ 19 *atan|------------------|
log\5 + x  - x /              \        19        /
---------------- + -------------------------------
       4                          38

$$\frac{\log{\left(x^{4} - x^{2} + 5 \right)}}{4} + \frac{\sqrt{19} \operatorname{atan}{\left(\frac{\sqrt{19} \left(2 x^{2} - 1\right)}{19} \right)}}{38}$$

log(5 + x^4 - x^2)/4 + sqrt(19)*atan(sqrt(19)*(-1 + 2*x^2)/19)/38

Respuesta numérica [src]

0.25*log(x^4 - x^2 + 5) + 0.114707866935281*atan((2*x^2 - 1)/sqrt(19))

0.25*log(x^4 - x^2 + 5) + 0.114707866935281*atan((2*x^2 - 1)/sqrt(19))

Unión de expresiones racionales [src]

                                        /  ____ /        2\\
      /     2 /      2\\       ____     |\/ 19 *\-1 + 2*x /|
19*log\5 + x *\-1 + x // + 2*\/ 19 *atan|------------------|
                                        \        19        /
------------------------------------------------------------
                             76

$$\frac{19 \log{\left(x^{2} \left(x^{2} - 1\right) + 5 \right)} + 2 \sqrt{19} \operatorname{atan}{\left(\frac{\sqrt{19} \left(2 x^{2} - 1\right)}{19} \right)}}{76}$$

(19*log(5 + x^2*(-1 + x^2)) + 2*sqrt(19)*atan(sqrt(19)*(-1 + 2*x^2)/19))/76

Denominador común [src]

                              /    ____       ____  2\
                     ____     |  \/ 19    2*\/ 19 *x |
   /     4    2\   \/ 19 *atan|- ------ + -----------|
log\5 + x  - x /              \    19          19    /
---------------- + -----------------------------------
       4                            38

$$\frac{\log{\left(x^{4} - x^{2} + 5 \right)}}{4} + \frac{\sqrt{19} \operatorname{atan}{\left(\frac{2 \sqrt{19} x^{2}}{19} - \frac{\sqrt{19}}{19} \right)}}{38}$$

log(5 + x^4 - x^2)/4 + sqrt(19)*atan(-sqrt(19)/19 + 2*sqrt(19)*x^2/19)/38

Denominador racional [src]

                                   /    ____       ____  2\
      /     4    2\       ____     |  \/ 19    2*\/ 19 *x |
19*log\5 + x  - x / + 2*\/ 19 *atan|- ------ + -----------|
                                   \    19          19    /
-----------------------------------------------------------
                             76

$$\frac{19 \log{\left(x^{4} - x^{2} + 5 \right)} + 2 \sqrt{19} \operatorname{atan}{\left(\frac{2 \sqrt{19} x^{2}}{19} - \frac{\sqrt{19}}{19} \right)}}{76}$$

(19*log(5 + x^4 - x^2) + 2*sqrt(19)*atan(-sqrt(19)/19 + 2*sqrt(19)*x^2/19))/76

Parte trigonométrica [src]

                              /  ____ /        2\\
                     ____     |\/ 19 *\-1 + 2*x /|
   /     4    2\   \/ 19 *atan|------------------|
log\5 + x  - x /              \        19        /
---------------- + -------------------------------
       4                          38

$$\frac{\log{\left(x^{4} - x^{2} + 5 \right)}}{4} + \frac{\sqrt{19} \operatorname{atan}{\left(\frac{\sqrt{19} \left(2 x^{2} - 1\right)}{19} \right)}}{38}$$

log(5 + x^4 - x^2)/4 + sqrt(19)*atan(sqrt(19)*(-1 + 2*x^2)/19)/38

Abrimos la expresión [src]

                              /   2    \
                     ____     |2*x  - 1|
                   \/ 19 *atan|--------|
   / 4    2    \              |   ____ |
log\x  - x  + 5/              \ \/ 19  /
---------------- + ---------------------
       4                     38

$$\frac{\log{\left(\left(x^{4} - x^{2}\right) + 5 \right)}}{4} + \frac{\sqrt{19} \operatorname{atan}{\left(\frac{2 x^{2} - 1}{\sqrt{19}} \right)}}{38}$$

log(x^4 - x^2 + 5)/4 + sqrt(19)*atan((2*x^2 - 1)/sqrt(19))/38

Compilar la expresión [src]

                              /   2    \
                     ____     |2*x  - 1|
                   \/ 19 *atan|--------|
   / 4    2    \              |   ____ |
log\x  - x  + 5/              \ \/ 19  /
---------------- + ---------------------
       4                     38

$$\frac{\log{\left(\left(x^{4} - x^{2}\right) + 5 \right)}}{4} + \frac{\sqrt{19} \operatorname{atan}{\left(\frac{2 x^{2} - 1}{\sqrt{19}} \right)}}{38}$$

log(x^4 - x^2 + 5)/4 + sqrt(19)*atan((2*x^2 - 1)/sqrt(19))/38

Combinatoria [src]

                              /    ____       ____  2\
                     ____     |  \/ 19    2*\/ 19 *x |
   /     4    2\   \/ 19 *atan|- ------ + -----------|
log\5 + x  - x /              \    19          19    /
---------------- + -----------------------------------
       4                            38

$$\frac{\log{\left(x^{4} - x^{2} + 5 \right)}}{4} + \frac{\sqrt{19} \operatorname{atan}{\left(\frac{2 \sqrt{19} x^{2}}{19} - \frac{\sqrt{19}}{19} \right)}}{38}$$

log(5 + x^4 - x^2)/4 + sqrt(19)*atan(-sqrt(19)/19 + 2*sqrt(19)*x^2/19)/38

Potencias [src]

                              /  ____ /        2\\
                     ____     |\/ 19 *\-1 + 2*x /|
   /     4    2\   \/ 19 *atan|------------------|
log\5 + x  - x /              \        19        /
---------------- + -------------------------------
       4                          38

$$\frac{\log{\left(x^{4} - x^{2} + 5 \right)}}{4} + \frac{\sqrt{19} \operatorname{atan}{\left(\frac{\sqrt{19} \left(2 x^{2} - 1\right)}{19} \right)}}{38}$$

                              /       /          2\\
                     ____     |  ____ |  1    2*x ||
   /     4    2\   \/ 19 *atan|\/ 19 *|- -- + ----||
log\5 + x  - x /              \       \  19    19 //
---------------- + ---------------------------------
       4                           38

$$\frac{\log{\left(x^{4} - x^{2} + 5 \right)}}{4} + \frac{\sqrt{19} \operatorname{atan}{\left(\sqrt{19} \left(\frac{2 x^{2}}{19} - \frac{1}{19}\right) \right)}}{38}$$

log(5 + x^4 - x^2)/4 + sqrt(19)*atan(sqrt(19)*(-1/19 + 2*x^2/19))/38

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¿Cómo vas a descomponer esta log(x^4-x^2+5)/4+atan((2*x^2-1)/sqrt(19))/(2*sqrt(19)) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta log(x^4-x^2+5)/4+atan((2x^2-1)/sqrt(19))/(2sqrt(19)) expresión en fracciones?