Sr Examen
¿Cómo vas a descomponer esta atan(x/10)/5-x/(100+x^2) expresión en fracciones?
Solución
Ha introducido
[src]
/x \
atan|--|
\10/ x
-------- - --------
5 2
100 + x
$$- \frac{x}{x^{2} + 100} + \frac{\operatorname{atan}{\left(\frac{x}{10} \right)}}{5}$$
atan(x/10)/5 - x/(100 + x^2)
Simplificación general
[src]
/ 2\ /x \
\100 + x /*atan|--|
\10/
-x + -------------------
5
------------------------
2
100 + x
$$\frac{- x + \frac{\left(x^{2} + 100\right) \operatorname{atan}{\left(\frac{x}{10} \right)}}{5}}{x^{2} + 100}$$
(-x + (100 + x^2)*atan(x/10)/5)/(100 + x^2)
Denominador racional
[src]
/ 2\ /x \
-5*x + \100 + x /*atan|--|
\10/
--------------------------
2
500 + 5*x
$$\frac{- 5 x + \left(x^{2} + 100\right) \operatorname{atan}{\left(\frac{x}{10} \right)}}{5 x^{2} + 500}$$
(-5*x + (100 + x^2)*atan(x/10))/(500 + 5*x^2)
Unión de expresiones racionales
[src]
/ 2\ /x \
-5*x + \100 + x /*atan|--|
\10/
--------------------------
/ 2\
5*\100 + x /
$$\frac{- 5 x + \left(x^{2} + 100\right) \operatorname{atan}{\left(\frac{x}{10} \right)}}{5 \left(x^{2} + 100\right)}$$
(-5*x + (100 + x^2)*atan(x/10))/(5*(100 + x^2))
Combinatoria
[src]
/x \ 2 /x \
-5*x + 100*atan|--| + x *atan|--|
\10/ \10/
---------------------------------
/ 2\
5*\100 + x /
$$\frac{x^{2} \operatorname{atan}{\left(\frac{x}{10} \right)} - 5 x + 100 \operatorname{atan}{\left(\frac{x}{10} \right)}}{5 \left(x^{2} + 100\right)}$$
(-5*x + 100*atan(x/10) + x^2*atan(x/10))/(5*(100 + x^2))