Sr Examen

Otras calculadoras

Resolución de integrales/ x^2+1/ x^3(x^2+1)^(3/2)

Integral de x^3(x^2+1)^(3/2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                  
  /                  
 |                   
 |             3/2   
 |   3 / 2    \      
 |  x *\x  + 1/    dx
 |                   
/                    
0
∫01x3(x2+1)32 dx\int\limits_{0}^{1} x^{3} \left(x^{2} + 1\right)^{\frac{3}{2}}\, dx 
Integral(x^3*(x^2 + 1)^(3/2), (x, 0, 1))
Solución detallada

  1. Hay varias maneras de calcular esta integral.

    Método #1

    1. Vuelva a escribir el integrando:

      x3(x2+1)32=x5x2+1+x3x2+1x^{3} \left(x^{2} + 1\right)^{\frac{3}{2}} = x^{5} \sqrt{x^{2} + 1} + x^{3} \sqrt{x^{2} + 1}

    2. Integramos término a término:

        TrigSubstitutionRule(theta=_theta, func=tan(_theta), rewritten=sin(_theta)**5/cos(_theta)**8, substep=RewriteRule(rewritten=(1 - cos(_theta)**2)**2*sin(_theta)/cos(_theta)**8, substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=(_u**4 - 2*_u**2 + 1)/_u**8, substep=RewriteRule(rewritten=_u**(-4) - 2/_u**6 + _u**(-8), substep=AddRule(substeps=[PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), ConstantTimesRule(constant=-2, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=-2/_u**6, symbol=_u), PowerRule(base=_u, exp=-8, context=_u**(-8), symbol=_u)], context=_u**(-4) - 2/_u**6 + _u**(-8), symbol=_u), context=(_u**4 - 2*_u**2 + 1)/_u**8, symbol=_u), context=(_u**4 - 2*_u**2 + 1)/_u**8, symbol=_u), context=(1 - cos(_theta)**2)**2*sin(_theta)/cos(_theta)**8, symbol=_theta), RewriteRule(rewritten=(sin(_theta)*cos(_theta)**4 - 2*sin(_theta)*cos(_theta)**2 + sin(_theta))/cos(_theta)**8, substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=(_u**4 - 2*_u**2 + 1)/_u**8, substep=RewriteRule(rewritten=_u**(-4) - 2/_u**6 + _u**(-8), substep=AddRule(substeps=[PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), ConstantTimesRule(constant=-2, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=-2/_u**6, symbol=_u), PowerRule(base=_u, exp=-8, context=_u**(-8), symbol=_u)], context=_u**(-4) - 2/_u**6 + _u**(-8), symbol=_u), context=(_u**4 - 2*_u**2 + 1)/_u**8, symbol=_u), context=(_u**4 - 2*_u**2 + 1)/_u**8, symbol=_u), context=(sin(_theta)*cos(_theta)**4 - 2*sin(_theta)*cos(_theta)**2 + sin(_theta))/cos(_theta)**8, symbol=_theta), RewriteRule(rewritten=sin(_theta)/cos(_theta)**4 - 2*sin(_theta)/cos(_theta)**6 + sin(_theta)/cos(_theta)**8, substep=AddRule(substeps=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-4), substep=PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), context=_u**(-4), symbol=_u), context=sin(_theta)/cos(_theta)**4, symbol=_theta), ConstantTimesRule(constant=-2, other=sin(_theta)/cos(_theta)**6, substep=URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=_u**(-6), symbol=_u), context=sin(_theta)/cos(_theta)**6, symbol=_theta), context=-2*sin(_theta)/cos(_theta)**6, symbol=_theta), URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-8), substep=PowerRule(base=_u, exp=-8, context=_u**(-8), symbol=_u), context=_u**(-8), symbol=_u), context=sin(_theta)/cos(_theta)**8, symbol=_theta)], context=sin(_theta)/cos(_theta)**4 - 2*sin(_theta)/cos(_theta)**6 + sin(_theta)/cos(_theta)**8, symbol=_theta), context=(sin(_theta)*cos(_theta)**4 - 2*sin(_theta)*cos(_theta)**2 + sin(_theta))/cos(_theta)**8, symbol=_theta)], context=(sin(_theta)*cos(_theta)**4 - 2*sin(_theta)*cos(_theta)**2 + sin(_theta))/cos(_theta)**8, symbol=_theta), context=(1 - cos(_theta)**2)**2*sin(_theta)/cos(_theta)**8, symbol=_theta), RewriteRule(rewritten=sin(_theta)/cos(_theta)**4 - 2*sin(_theta)/cos(_theta)**6 + sin(_theta)/cos(_theta)**8, substep=AddRule(substeps=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-4), substep=PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), context=_u**(-4), symbol=_u), context=sin(_theta)/cos(_theta)**4, symbol=_theta), ConstantTimesRule(constant=-2, other=sin(_theta)/cos(_theta)**6, substep=URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=_u**(-6), symbol=_u), context=sin(_theta)/cos(_theta)**6, symbol=_theta), context=-2*sin(_theta)/cos(_theta)**6, symbol=_theta), URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-8), substep=PowerRule(base=_u, exp=-8, context=_u**(-8), symbol=_u), context=_u**(-8), symbol=_u), context=sin(_theta)/cos(_theta)**8, symbol=_theta)], context=sin(_theta)/cos(_theta)**4 - 2*sin(_theta)/cos(_theta)**6 + sin(_theta)/cos(_theta)**8, symbol=_theta), context=(1 - cos(_theta)**2)**2*sin(_theta)/cos(_theta)**8, symbol=_theta)], context=(1 - cos(_theta)**2)**2*sin(_theta)/cos(_theta)**8, symbol=_theta), context=sin(_theta)**5/cos(_theta)**8, symbol=_theta), restriction=True, context=x**5*sqrt(x**2 + 1), symbol=x)

        TrigSubstitutionRule(theta=_theta, func=tan(_theta), rewritten=sin(_theta)**3/cos(_theta)**6, substep=RewriteRule(rewritten=(1 - cos(_theta)**2)*sin(_theta)/cos(_theta)**6, substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=cos(_theta), constant=1, substep=RewriteRule(rewritten=_u**(-4) - 1/_u**6, substep=AddRule(substeps=[PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=-1/_u**6, symbol=_u)], context=_u**(-4) - 1/_u**6, symbol=_u), context=(_u**2 - 1)/_u**6, symbol=_u), context=(1 - cos(_theta)**2)*sin(_theta)/cos(_theta)**6, symbol=_theta), RewriteRule(rewritten=-(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, substep=ConstantTimesRule(constant=-1, other=(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=(_u**2 - 1)/_u**6, substep=RewriteRule(rewritten=_u**(-4) - 1/_u**6, substep=AddRule(substeps=[PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=-1/_u**6, symbol=_u)], context=_u**(-4) - 1/_u**6, symbol=_u), context=(_u**2 - 1)/_u**6, symbol=_u), context=(_u**2 - 1)/_u**6, symbol=_u), context=(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, symbol=_theta), RewriteRule(rewritten=sin(_theta)/cos(_theta)**4 - sin(_theta)/cos(_theta)**6, substep=AddRule(substeps=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-4), substep=PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), context=_u**(-4), symbol=_u), context=sin(_theta)/cos(_theta)**4, symbol=_theta), ConstantTimesRule(constant=-1, other=sin(_theta)/cos(_theta)**6, substep=URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=_u**(-6), symbol=_u), context=sin(_theta)/cos(_theta)**6, symbol=_theta), context=-sin(_theta)/cos(_theta)**6, symbol=_theta)], context=sin(_theta)/cos(_theta)**4 - sin(_theta)/cos(_theta)**6, symbol=_theta), context=(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, symbol=_theta)], context=(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, symbol=_theta), context=-(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, symbol=_theta), context=(1 - cos(_theta)**2)*sin(_theta)/cos(_theta)**6, symbol=_theta), RewriteRule(rewritten=-sin(_theta)/cos(_theta)**4 + sin(_theta)/cos(_theta)**6, substep=AddRule(substeps=[ConstantTimesRule(constant=-1, other=sin(_theta)/cos(_theta)**4, substep=URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-4), substep=PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), context=_u**(-4), symbol=_u), context=sin(_theta)/cos(_theta)**4, symbol=_theta), context=-sin(_theta)/cos(_theta)**4, symbol=_theta), URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=_u**(-6), symbol=_u), context=sin(_theta)/cos(_theta)**6, symbol=_theta)], context=-sin(_theta)/cos(_theta)**4 + sin(_theta)/cos(_theta)**6, symbol=_theta), context=(1 - cos(_theta)**2)*sin(_theta)/cos(_theta)**6, symbol=_theta)], context=(1 - cos(_theta)**2)*sin(_theta)/cos(_theta)**6, symbol=_theta), context=sin(_theta)**3/cos(_theta)**6, symbol=_theta), restriction=True, context=x**3*sqrt(x**2 + 1), symbol=x)

      El resultado es: (x2+1)727−(x2+1)525\frac{\left(x^{2} + 1\right)^{\frac{7}{2}}}{7} - \frac{\left(x^{2} + 1\right)^{\frac{5}{2}}}{5}

    Método #2

    1. Vuelva a escribir el integrando:

      x3(x2+1)32=x5x2+1+x3x2+1x^{3} \left(x^{2} + 1\right)^{\frac{3}{2}} = x^{5} \sqrt{x^{2} + 1} + x^{3} \sqrt{x^{2} + 1}

    2. Integramos término a término:

        TrigSubstitutionRule(theta=_theta, func=tan(_theta), rewritten=sin(_theta)**5/cos(_theta)**8, substep=RewriteRule(rewritten=(1 - cos(_theta)**2)**2*sin(_theta)/cos(_theta)**8, substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=(_u**4 - 2*_u**2 + 1)/_u**8, substep=RewriteRule(rewritten=_u**(-4) - 2/_u**6 + _u**(-8), substep=AddRule(substeps=[PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), ConstantTimesRule(constant=-2, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=-2/_u**6, symbol=_u), PowerRule(base=_u, exp=-8, context=_u**(-8), symbol=_u)], context=_u**(-4) - 2/_u**6 + _u**(-8), symbol=_u), context=(_u**4 - 2*_u**2 + 1)/_u**8, symbol=_u), context=(_u**4 - 2*_u**2 + 1)/_u**8, symbol=_u), context=(1 - cos(_theta)**2)**2*sin(_theta)/cos(_theta)**8, symbol=_theta), RewriteRule(rewritten=(sin(_theta)*cos(_theta)**4 - 2*sin(_theta)*cos(_theta)**2 + sin(_theta))/cos(_theta)**8, substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=(_u**4 - 2*_u**2 + 1)/_u**8, substep=RewriteRule(rewritten=_u**(-4) - 2/_u**6 + _u**(-8), substep=AddRule(substeps=[PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), ConstantTimesRule(constant=-2, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=-2/_u**6, symbol=_u), PowerRule(base=_u, exp=-8, context=_u**(-8), symbol=_u)], context=_u**(-4) - 2/_u**6 + _u**(-8), symbol=_u), context=(_u**4 - 2*_u**2 + 1)/_u**8, symbol=_u), context=(_u**4 - 2*_u**2 + 1)/_u**8, symbol=_u), context=(sin(_theta)*cos(_theta)**4 - 2*sin(_theta)*cos(_theta)**2 + sin(_theta))/cos(_theta)**8, symbol=_theta), RewriteRule(rewritten=sin(_theta)/cos(_theta)**4 - 2*sin(_theta)/cos(_theta)**6 + sin(_theta)/cos(_theta)**8, substep=AddRule(substeps=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-4), substep=PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), context=_u**(-4), symbol=_u), context=sin(_theta)/cos(_theta)**4, symbol=_theta), ConstantTimesRule(constant=-2, other=sin(_theta)/cos(_theta)**6, substep=URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=_u**(-6), symbol=_u), context=sin(_theta)/cos(_theta)**6, symbol=_theta), context=-2*sin(_theta)/cos(_theta)**6, symbol=_theta), URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-8), substep=PowerRule(base=_u, exp=-8, context=_u**(-8), symbol=_u), context=_u**(-8), symbol=_u), context=sin(_theta)/cos(_theta)**8, symbol=_theta)], context=sin(_theta)/cos(_theta)**4 - 2*sin(_theta)/cos(_theta)**6 + sin(_theta)/cos(_theta)**8, symbol=_theta), context=(sin(_theta)*cos(_theta)**4 - 2*sin(_theta)*cos(_theta)**2 + sin(_theta))/cos(_theta)**8, symbol=_theta)], context=(sin(_theta)*cos(_theta)**4 - 2*sin(_theta)*cos(_theta)**2 + sin(_theta))/cos(_theta)**8, symbol=_theta), context=(1 - cos(_theta)**2)**2*sin(_theta)/cos(_theta)**8, symbol=_theta), RewriteRule(rewritten=sin(_theta)/cos(_theta)**4 - 2*sin(_theta)/cos(_theta)**6 + sin(_theta)/cos(_theta)**8, substep=AddRule(substeps=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-4), substep=PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), context=_u**(-4), symbol=_u), context=sin(_theta)/cos(_theta)**4, symbol=_theta), ConstantTimesRule(constant=-2, other=sin(_theta)/cos(_theta)**6, substep=URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=_u**(-6), symbol=_u), context=sin(_theta)/cos(_theta)**6, symbol=_theta), context=-2*sin(_theta)/cos(_theta)**6, symbol=_theta), URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-8), substep=PowerRule(base=_u, exp=-8, context=_u**(-8), symbol=_u), context=_u**(-8), symbol=_u), context=sin(_theta)/cos(_theta)**8, symbol=_theta)], context=sin(_theta)/cos(_theta)**4 - 2*sin(_theta)/cos(_theta)**6 + sin(_theta)/cos(_theta)**8, symbol=_theta), context=(1 - cos(_theta)**2)**2*sin(_theta)/cos(_theta)**8, symbol=_theta)], context=(1 - cos(_theta)**2)**2*sin(_theta)/cos(_theta)**8, symbol=_theta), context=sin(_theta)**5/cos(_theta)**8, symbol=_theta), restriction=True, context=x**5*sqrt(x**2 + 1), symbol=x)

        TrigSubstitutionRule(theta=_theta, func=tan(_theta), rewritten=sin(_theta)**3/cos(_theta)**6, substep=RewriteRule(rewritten=(1 - cos(_theta)**2)*sin(_theta)/cos(_theta)**6, substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=cos(_theta), constant=1, substep=RewriteRule(rewritten=_u**(-4) - 1/_u**6, substep=AddRule(substeps=[PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=-1/_u**6, symbol=_u)], context=_u**(-4) - 1/_u**6, symbol=_u), context=(_u**2 - 1)/_u**6, symbol=_u), context=(1 - cos(_theta)**2)*sin(_theta)/cos(_theta)**6, symbol=_theta), RewriteRule(rewritten=-(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, substep=ConstantTimesRule(constant=-1, other=(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=(_u**2 - 1)/_u**6, substep=RewriteRule(rewritten=_u**(-4) - 1/_u**6, substep=AddRule(substeps=[PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=-1/_u**6, symbol=_u)], context=_u**(-4) - 1/_u**6, symbol=_u), context=(_u**2 - 1)/_u**6, symbol=_u), context=(_u**2 - 1)/_u**6, symbol=_u), context=(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, symbol=_theta), RewriteRule(rewritten=sin(_theta)/cos(_theta)**4 - sin(_theta)/cos(_theta)**6, substep=AddRule(substeps=[URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-4), substep=PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), context=_u**(-4), symbol=_u), context=sin(_theta)/cos(_theta)**4, symbol=_theta), ConstantTimesRule(constant=-1, other=sin(_theta)/cos(_theta)**6, substep=URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=_u**(-6), symbol=_u), context=sin(_theta)/cos(_theta)**6, symbol=_theta), context=-sin(_theta)/cos(_theta)**6, symbol=_theta)], context=sin(_theta)/cos(_theta)**4 - sin(_theta)/cos(_theta)**6, symbol=_theta), context=(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, symbol=_theta)], context=(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, symbol=_theta), context=-(sin(_theta)*cos(_theta)**2 - sin(_theta))/cos(_theta)**6, symbol=_theta), context=(1 - cos(_theta)**2)*sin(_theta)/cos(_theta)**6, symbol=_theta), RewriteRule(rewritten=-sin(_theta)/cos(_theta)**4 + sin(_theta)/cos(_theta)**6, substep=AddRule(substeps=[ConstantTimesRule(constant=-1, other=sin(_theta)/cos(_theta)**4, substep=URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-4), substep=PowerRule(base=_u, exp=-4, context=_u**(-4), symbol=_u), context=_u**(-4), symbol=_u), context=sin(_theta)/cos(_theta)**4, symbol=_theta), context=-sin(_theta)/cos(_theta)**4, symbol=_theta), URule(u_var=_u, u_func=cos(_theta), constant=-1, substep=ConstantTimesRule(constant=-1, other=_u**(-6), substep=PowerRule(base=_u, exp=-6, context=_u**(-6), symbol=_u), context=_u**(-6), symbol=_u), context=sin(_theta)/cos(_theta)**6, symbol=_theta)], context=-sin(_theta)/cos(_theta)**4 + sin(_theta)/cos(_theta)**6, symbol=_theta), context=(1 - cos(_theta)**2)*sin(_theta)/cos(_theta)**6, symbol=_theta)], context=(1 - cos(_theta)**2)*sin(_theta)/cos(_theta)**6, symbol=_theta), context=sin(_theta)**3/cos(_theta)**6, symbol=_theta), restriction=True, context=x**3*sqrt(x**2 + 1), symbol=x)

      El resultado es: (x2+1)727−(x2+1)525\frac{\left(x^{2} + 1\right)^{\frac{7}{2}}}{7} - \frac{\left(x^{2} + 1\right)^{\frac{5}{2}}}{5}

  2. Ahora simplificar:

    (x2+1)52(5x2−2)35\frac{\left(x^{2} + 1\right)^{\frac{5}{2}} \left(5 x^{2} - 2\right)}{35}

  3. Añadimos la constante de integración:

    (x2+1)52(5x2−2)35+constant\frac{\left(x^{2} + 1\right)^{\frac{5}{2}} \left(5 x^{2} - 2\right)}{35}+ \mathrm{constant}

Respuesta:

(x2+1)52(5x2−2)35+constant\frac{\left(x^{2} + 1\right)^{\frac{5}{2}} \left(5 x^{2} - 2\right)}{35}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
  /                                                 
 |                                 5/2           7/2
 |            3/2          /     2\      /     2\   
 |  3 / 2    \             \1 + x /      \1 + x /   
 | x *\x  + 1/    dx = C - ----------- + -----------
 |                              5             7     
/
∫x3(x2+1)32 dx=C+(x2+1)727−(x2+1)525\int x^{3} \left(x^{2} + 1\right)^{\frac{3}{2}}\, dx = C + \frac{\left(x^{2} + 1\right)^{\frac{7}{2}}}{7} - \frac{\left(x^{2} + 1\right)^{\frac{5}{2}}}{5}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.905-5
Trazar el gráfico f(x)
Respuesta [src] 
          ___
2    12*\/ 2 
-- + --------
35      35
235+12235\frac{2}{35} + \frac{12 \sqrt{2}}{35} 
=
= 
          ___
2    12*\/ 2 
-- + --------
35      35
235+12235\frac{2}{35} + \frac{12 \sqrt{2}}{35} 
2/35 + 12*sqrt(2)/35
Respuesta numérica [src] 
0.542016078527918
0.542016078527918

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

    © Sr Examen – Калькулятор