Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
asin(x/sqrt(1+x^2))^2*(1/(sqrt(1+x^2))-x^2/(1+x^2)^(3/2))/sqrt(1-x^2/(1+x^2))
¿Cómo vas a descomponer esta asin(x/sqrt(1+x^2))^2*(1/(sqrt(1+x^2))-x^2/(1+x^2)^(3/2))/sqrt(1-x^2/(1+x^2)) expresión en fracciones?
Solución
Ha introducido
[src]
/ 2 \
2/ x \ | 1 x |
asin |-----------|*|----------- - -----------|
| ________| | ________ 3/2|
| / 2 | | / 2 / 2\ |
\\/ 1 + x / \\/ 1 + x \1 + x / /
----------------------------------------------
____________
/ 2
/ x
/ 1 - ------
/ 2
\/ 1 + x
$$\frac{\left(- \frac{x^{2}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x^{2} + 1}}\right) \operatorname{asin}^{2}{\left(\frac{x}{\sqrt{x^{2} + 1}} \right)}}{\sqrt{- \frac{x^{2}}{x^{2} + 1} + 1}}$$
(asin(x/sqrt(1 + x^2))^2*(1/(sqrt(1 + x^2)) - x^2/(1 + x^2)^(3/2)))/sqrt(1 - x^2/(1 + x^2))
Simplificación general
[src]
2/ x \
asin |-----------|
| ________|
| / 2 |
\\/ 1 + x /
-------------------------
________ 3/2
/ 1 / 2\
/ ------ *\1 + x /
/ 2
\/ 1 + x
$$\frac{\operatorname{asin}^{2}{\left(\frac{x}{\sqrt{x^{2} + 1}} \right)}}{\left(x^{2} + 1\right)^{\frac{3}{2}} \sqrt{\frac{1}{x^{2} + 1}}}$$
asin(x/sqrt(1 + x^2))^2/(sqrt(1/(1 + x^2))*(1 + x^2)^(3/2))
Respuesta numérica
[src]
(1.0 - x^2/(1.0 + x^2))^(-0.5)*asin(x/sqrt(1 + x^2))^2*((1.0 + x^2)^(-0.5) - x^2*(1.0 + x^2)^(-1.5))
(1.0 - x^2/(1.0 + x^2))^(-0.5)*asin(x/sqrt(1 + x^2))^2*((1.0 + x^2)^(-0.5) - x^2*(1.0 + x^2)^(-1.5))
Unión de expresiones racionales
[src]
2/ x \
asin |-----------|
| ________|
| / 2 |
\\/ 1 + x /
-------------------------
________ 3/2
/ 1 / 2\
/ ------ *\1 + x /
/ 2
\/ 1 + x
$$\frac{\operatorname{asin}^{2}{\left(\frac{x}{\sqrt{x^{2} + 1}} \right)}}{\left(x^{2} + 1\right)^{\frac{3}{2}} \sqrt{\frac{1}{x^{2} + 1}}}$$
asin(x/sqrt(1 + x^2))^2/(sqrt(1/(1 + x^2))*(1 + x^2)^(3/2))
Denominador común
[src]
____________
/ 2
/ x 2/ x \
/ 1 - ------ *asin |-----------|
/ 2 | ________|
\/ 1 + x | / 2 |
\\/ 1 + x /
-------------------------------------
________
/ 2
\/ 1 + x
$$\frac{\sqrt{- \frac{x^{2}}{x^{2} + 1} + 1} \operatorname{asin}^{2}{\left(\frac{x}{\sqrt{x^{2} + 1}} \right)}}{\sqrt{x^{2} + 1}}$$
sqrt(1 - x^2/(1 + x^2))*asin(x/sqrt(1 + x^2))^2/sqrt(1 + x^2)
Denominador racional
[src]
____________ / ________\ ____________ / ________\
3/2 / 2 | / 2 | ________ / 2 | / 2 |
/ 2\ / x 2|x*\/ 1 + x | 2 / 2 / x 2|x*\/ 1 + x |
- \1 + x / * / 1 - ------ *asin |-------------| + x *\/ 1 + x * / 1 - ------ *asin |-------------|
/ 2 | 2 | / 2 | 2 |
\/ 1 + x \ 1 + x / \/ 1 + x \ 1 + x /
--------------------------------------------------------------------------------------------------------------
2 / 2 \
/ 2\ | x |
\1 + x / *|-1 + ------|
| 2|
\ 1 + x /
$$\frac{x^{2} \sqrt{x^{2} + 1} \sqrt{- \frac{x^{2}}{x^{2} + 1} + 1} \operatorname{asin}^{2}{\left(\frac{x \sqrt{x^{2} + 1}}{x^{2} + 1} \right)} - \left(x^{2} + 1\right)^{\frac{3}{2}} \sqrt{- \frac{x^{2}}{x^{2} + 1} + 1} \operatorname{asin}^{2}{\left(\frac{x \sqrt{x^{2} + 1}}{x^{2} + 1} \right)}}{\left(x^{2} + 1\right)^{2} \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}$$
(-(1 + x^2)^(3/2)*sqrt(1 - x^2/(1 + x^2))*asin(x*sqrt(1 + x^2)/(1 + x^2))^2 + x^2*sqrt(1 + x^2)*sqrt(1 - x^2/(1 + x^2))*asin(x*sqrt(1 + x^2)/(1 + x^2))^2)/((1 + x^2)^2*(-1 + x^2/(1 + x^2)))
Combinatoria
[src]
2/ x \
asin |-----------|
| ________|
| / 2 |
\\/ 1 + x /
-------------------------
________ 3/2
/ 1 / 2\
/ ------ *\1 + x /
/ 2
\/ 1 + x
$$\frac{\operatorname{asin}^{2}{\left(\frac{x}{\sqrt{x^{2} + 1}} \right)}}{\left(x^{2} + 1\right)^{\frac{3}{2}} \sqrt{\frac{1}{x^{2} + 1}}}$$
asin(x/sqrt(1 + x^2))^2/(sqrt(1/(1 + x^2))*(1 + x^2)^(3/2))