Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
asin(x)/(1-x^2)^(3/2)+3*x*(sqrt(1-x^2)+x*asin(x))/(1-x^2)^(5/2)
¿Cómo vas a descomponer esta asin(x)/(1-x^2)^(3/2)+3*x*(sqrt(1-x^2)+x*asin(x))/(1-x^2)^(5/2) expresión en fracciones?
Solución
Ha introducido
[src]
/ ________ \
| / 2 |
asin(x) 3*x*\\/ 1 - x + x*asin(x)/
----------- + -----------------------------
3/2 5/2
/ 2\ / 2\
\1 - x / \1 - x /
$$\frac{3 x \left(x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}\right)}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}$$
asin(x)/(1 - x^2)^(3/2) + ((3*x)*(sqrt(1 - x^2) + x*asin(x)))/(1 - x^2)^(5/2)
Simplificación general
[src]
/ ________ \
/ 2\ | / 2 |
\1 - x /*asin(x) + 3*x*\\/ 1 - x + x*asin(x)/
------------------------------------------------
5/2
/ 2\
\1 - x /
$$\frac{3 x \left(x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}\right) + \left(1 - x^{2}\right) \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}}$$
((1 - x^2)*asin(x) + 3*x*(sqrt(1 - x^2) + x*asin(x)))/(1 - x^2)^(5/2)
Respuesta numérica
[src]
(1.0 - x^2)^(-1.5)*asin(x) + 3.0*x*(1.0 - x^2)^(-2.5)*((1.0 - x^2)^0.5 + x*asin(x))
(1.0 - x^2)^(-1.5)*asin(x) + 3.0*x*(1.0 - x^2)^(-2.5)*((1.0 - x^2)^0.5 + x*asin(x))
Denominador común
[src]
________
2 / 2
2*x *asin(x) + 3*x*\/ 1 - x + asin(x)
-----------------------------------------------
________ ________ ________
/ 2 4 / 2 2 / 2
\/ 1 - x + x *\/ 1 - x - 2*x *\/ 1 - x
$$\frac{2 x^{2} \operatorname{asin}{\left(x \right)} + 3 x \sqrt{1 - x^{2}} + \operatorname{asin}{\left(x \right)}}{x^{4} \sqrt{1 - x^{2}} - 2 x^{2} \sqrt{1 - x^{2}} + \sqrt{1 - x^{2}}}$$
(2*x^2*asin(x) + 3*x*sqrt(1 - x^2) + asin(x))/(sqrt(1 - x^2) + x^4*sqrt(1 - x^2) - 2*x^2*sqrt(1 - x^2))
Denominador racional
[src]
5/2 3/2 / ________ \
/ 2\ / 2\ | / 2 |
\1 - x / *asin(x) + 3*x*\1 - x / *\\/ 1 - x + x*asin(x)/
---------------------------------------------------------------
4
/ 2\
\1 - x /
$$\frac{3 x \left(1 - x^{2}\right)^{\frac{3}{2}} \left(x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}\right) + \left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{4}}$$
((1 - x^2)^(5/2)*asin(x) + 3*x*(1 - x^2)^(3/2)*(sqrt(1 - x^2) + x*asin(x)))/(1 - x^2)^4
Unión de expresiones racionales
[src]
/ ________ \
/ 2\ | / 2 |
\1 - x /*asin(x) + 3*x*\\/ 1 - x + x*asin(x)/
------------------------------------------------
5/2
/ 2\
\1 - x /
$$\frac{3 x \left(x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}\right) + \left(1 - x^{2}\right) \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}}$$
((1 - x^2)*asin(x) + 3*x*(sqrt(1 - x^2) + x*asin(x)))/(1 - x^2)^(5/2)
Combinatoria
[src]
________
2 / 2
2*x *asin(x) + 3*x*\/ 1 - x + asin(x)
----------------------------------------
5/2
(-(1 + x)*(-1 + x))
$$\frac{2 x^{2} \operatorname{asin}{\left(x \right)} + 3 x \sqrt{1 - x^{2}} + \operatorname{asin}{\left(x \right)}}{\left(- \left(x - 1\right) \left(x + 1\right)\right)^{\frac{5}{2}}}$$
(2*x^2*asin(x) + 3*x*sqrt(1 - x^2) + asin(x))/(-(1 + x)*(-1 + x))^(5/2)