Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
atan((2*x)/15)/30+7*log(x-1)+3^(5*x+6)/(5*log(3))
¿Cómo vas a descomponer esta atan((2*x)/15)/30+7*log(x-1)+3^(5*x+6)/(5*log(3)) expresión en fracciones?
Solución
Ha introducido
[src]
/2*x\
atan|---| 5*x + 6
\ 15/ 3
--------- + 7*log(x - 1) + --------
30 5*log(3)
$$\frac{3^{5 x + 6}}{5 \log{\left(3 \right)}} + \left(7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30}\right)$$
atan((2*x)/15)/30 + 7*log(x - 1) + 3^(5*x + 6)/((5*log(3)))
Simplificación general
[src]
/2*x\
atan|---| 5*x
\ 15/ 729*3
7*log(-1 + x) + --------- + --------
30 5*log(3)
$$\frac{729 \cdot 3^{5 x}}{5 \log{\left(3 \right)}} + 7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30}$$
7*log(-1 + x) + atan(2*x/15)/30 + 729*3^(5*x)/(5*log(3))
Respuesta numérica
[src]
7.0*log(x - 1) + 0.0333333333333333*atan((2*x)/15) + 0.182047845325367*3.0^(6.0 + 5.0*x)
7.0*log(x - 1) + 0.0333333333333333*atan((2*x)/15) + 0.182047845325367*3.0^(6.0 + 5.0*x)
Potencias
[src]
/2*x\
atan|---| 6 + 5*x
\ 15/ 3
7*log(-1 + x) + --------- + --------
30 5*log(3)
$$\frac{3^{5 x + 6}}{5 \log{\left(3 \right)}} + 7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30}$$
7*log(-1 + x) + atan(2*x/15)/30 + 3^(6 + 5*x)/(5*log(3))
Parte trigonométrica
[src]
/2*x\
atan|---| 6 + 5*x
\ 15/ 3
7*log(-1 + x) + --------- + --------
30 5*log(3)
$$\frac{3^{5 x + 6}}{5 \log{\left(3 \right)}} + 7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30}$$
7*log(-1 + x) + atan(2*x/15)/30 + 3^(6 + 5*x)/(5*log(3))
Denominador común
[src]
/2*x\
atan|---| 5*x
\ 15/ 729*3
7*log(-1 + x) + --------- + --------
30 5*log(3)
$$\frac{729 \cdot 3^{5 x}}{5 \log{\left(3 \right)}} + 7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30}$$
7*log(-1 + x) + atan(2*x/15)/30 + 729*3^(5*x)/(5*log(3))
Denominador racional
[src]
6 + 5*x /2*x\
30*3 + 5*atan|---|*log(3) + 1050*log(3)*log(-1 + x)
\ 15/
----------------------------------------------------------
150*log(3)
$$\frac{30 \cdot 3^{5 x + 6} + 1050 \log{\left(3 \right)} \log{\left(x - 1 \right)} + 5 \log{\left(3 \right)} \operatorname{atan}{\left(\frac{2 x}{15} \right)}}{150 \log{\left(3 \right)}}$$
(30*3^(6 + 5*x) + 5*atan(2*x/15)*log(3) + 1050*log(3)*log(-1 + x))/(150*log(3))
Combinatoria
[src]
5*x /2*x\
4374*3 + atan|---|*log(3) + 210*log(3)*log(-1 + x)
\ 15/
-----------------------------------------------------
30*log(3)
$$\frac{4374 \cdot 3^{5 x} + 210 \log{\left(3 \right)} \log{\left(x - 1 \right)} + \log{\left(3 \right)} \operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30 \log{\left(3 \right)}}$$
(4374*3^(5*x) + atan(2*x/15)*log(3) + 210*log(3)*log(-1 + x))/(30*log(3))
Unión de expresiones racionales
[src]
6 + 5*x / /2*x\\
6*3 + |210*log(-1 + x) + atan|---||*log(3)
\ \ 15//
-------------------------------------------------
30*log(3)
$$\frac{6 \cdot 3^{5 x + 6} + \left(210 \log{\left(x - 1 \right)} + \operatorname{atan}{\left(\frac{2 x}{15} \right)}\right) \log{\left(3 \right)}}{30 \log{\left(3 \right)}}$$
(6*3^(6 + 5*x) + (210*log(-1 + x) + atan(2*x/15))*log(3))/(30*log(3))
Compilar la expresión
[src]
/2*x\
atan|---| 5*x + 6
\ 15/ 3
7*log(x - 1) + --------- + --------
30 5*log(3)
$$\frac{3^{5 x + 6}}{5 \log{\left(3 \right)}} + 7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30}$$
7*log(x - 1) + atan((2*x)/15)/30 + 3^(5*x + 6)/(5*log(3))