Sr Examen

Otras calculadoras

Resolución de integrales/ x^2+y/ 1/(1+(x^2+y^2)^2)

Integral de 1/(1+(x^2+y^2)^2) dy

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                  
  /                  
 |                   
 |        1          
 |  -------------- dy
 |               2   
 |      / 2    2\    
 |  1 + \x  + y /    
 |                   
/                    
0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} + y^{2}\right)^{2} + 1}\, dy$$ 
Integral(1/(1 + (x^2 + y^2)^2), (y, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                     
 |                                                                                                                      
 |       1                        / 4 /           4\       2  2                /             4         2  3       6  3\\
 | -------------- dy = C + RootSum\t *\256 + 256*x / - 32*x *t  + 1, t -> t*log\y + 4*t - 4*x *t + 64*x *t  + 64*x *t //
 |              2                                                                                                       
 |     / 2    2\                                                                                                        
 | 1 + \x  + y /                                                                                                        
 |                                                                                                                      
/
$$\int \frac{1}{\left(x^{2} + y^{2}\right)^{2} + 1}\, dy = C + \operatorname{RootSum} {\left(t^{4} \left(256 x^{4} + 256\right) - 32 t^{2} x^{2} + 1, \left( t \mapsto t \log{\left(64 t^{3} x^{6} + 64 t^{3} x^{2} - 4 t x^{4} + 4 t + y \right)} \right)\right)}$$
Simplificar
Respuesta [src] 
         / 4 /           4\       2  2                /         4         2  3       6  3\\          / 4 /           4\       2  2                /             4         2  3       6  3\\
- RootSum\t *\256 + 256*x / - 32*x *t  + 1, t -> t*log\4*t - 4*x *t + 64*x *t  + 64*x *t // + RootSum\t *\256 + 256*x / - 32*x *t  + 1, t -> t*log\1 + 4*t - 4*x *t + 64*x *t  + 64*x *t //
$$- \operatorname{RootSum} {\left(t^{4} \left(256 x^{4} + 256\right) - 32 t^{2} x^{2} + 1, \left( t \mapsto t \log{\left(64 t^{3} x^{6} + 64 t^{3} x^{2} - 4 t x^{4} + 4 t \right)} \right)\right)} + \operatorname{RootSum} {\left(t^{4} \left(256 x^{4} + 256\right) - 32 t^{2} x^{2} + 1, \left( t \mapsto t \log{\left(64 t^{3} x^{6} + 64 t^{3} x^{2} - 4 t x^{4} + 4 t + 1 \right)} \right)\right)}$$ 
=
= 
         / 4 /           4\       2  2                /         4         2  3       6  3\\          / 4 /           4\       2  2                /             4         2  3       6  3\\
- RootSum\t *\256 + 256*x / - 32*x *t  + 1, t -> t*log\4*t - 4*x *t + 64*x *t  + 64*x *t // + RootSum\t *\256 + 256*x / - 32*x *t  + 1, t -> t*log\1 + 4*t - 4*x *t + 64*x *t  + 64*x *t //
$$- \operatorname{RootSum} {\left(t^{4} \left(256 x^{4} + 256\right) - 32 t^{2} x^{2} + 1, \left( t \mapsto t \log{\left(64 t^{3} x^{6} + 64 t^{3} x^{2} - 4 t x^{4} + 4 t \right)} \right)\right)} + \operatorname{RootSum} {\left(t^{4} \left(256 x^{4} + 256\right) - 32 t^{2} x^{2} + 1, \left( t \mapsto t \log{\left(64 t^{3} x^{6} + 64 t^{3} x^{2} - 4 t x^{4} + 4 t + 1 \right)} \right)\right)}$$ 
-RootSum(_t^4*(256 + 256*x^4) - 32*x^2*_t^2 + 1, Lambda(_t, _t*log(4*_t - 4*x^4*_t + 64*x^2*_t^3 + 64*x^6*_t^3))) + RootSum(_t^4*(256 + 256*x^4) - 32*x^2*_t^2 + 1, Lambda(_t, _t*log(1 + 4*_t - 4*x^4*_t + 64*x^2*_t^3 + 64*x^6*_t^3)))

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

    © Sr Examen – Калькулятор