Sr Examen
Integral de 1/((x+a)^2*sqrt(x+c)) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------------ dx | 2 _______ | (x + a) *\/ x + c | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(a + x\right)^{2} \sqrt{c + x}}\, dx$$
Integral(1/((x + a)^2*sqrt(x + c)), (x, 0, 1))
Respuesta
[src]
/ ___________________\ / ___________________\
_______________________ |\/ polar_lift(c - a) | ___________________________ |\/ polar_lift(c - a) |
a*\/ a + polar_lift(c - a) *asinh|---------------------| \/ 1 + a + polar_lift(c - a) *(1 + a)*asinh|---------------------|
___________________ ___________________ ___________________ ___________________ | ___ | | _______ |
c*\/ polar_lift(c - a) \/ polar_lift(c - a) *(1 + a) a*\/ polar_lift(c - a) c*\/ polar_lift(c - a) \ \/ a / \ \/ 1 + a /
----------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------
___________________________ ___________________ ___________________________ ___________________ ___________________________ ___________________ ___________________________ ___________________ ___________________________ ___________________ ___________________________ ___________________ 2 _______________________ ___________________ _______________________ ___________________ 2 _______________________ ___________________ _______________________ ___________________ ___________________________ ___________________ ___________________________ ___________________
a*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) - c*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) a*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) - c*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) a*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) - c*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) a *\/ a + polar_lift(c - a) *\/ polar_lift(c - a) - a*c*\/ a + polar_lift(c - a) *\/ polar_lift(c - a) a *\/ a + polar_lift(c - a) *\/ polar_lift(c - a) - a*c*\/ a + polar_lift(c - a) *\/ polar_lift(c - a) a*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) - c*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a)
$$\frac{a \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)}} \operatorname{asinh}{\left(\frac{\sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{\sqrt{a}} \right)}}{a^{2} \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)}} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - a c \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)}} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}} - \frac{a \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{a \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - c \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}} + \frac{c \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{a \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - c \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}} - \frac{c \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{a^{2} \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)}} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - a c \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)}} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}} - \frac{\left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \operatorname{asinh}{\left(\frac{\sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{\sqrt{a + 1}} \right)}}{a \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - c \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}} + \frac{\left(a + 1\right) \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{a \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - c \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}$$
=
=
/ ___________________\ / ___________________\
_______________________ |\/ polar_lift(c - a) | ___________________________ |\/ polar_lift(c - a) |
a*\/ a + polar_lift(c - a) *asinh|---------------------| \/ 1 + a + polar_lift(c - a) *(1 + a)*asinh|---------------------|
___________________ ___________________ ___________________ ___________________ | ___ | | _______ |
c*\/ polar_lift(c - a) \/ polar_lift(c - a) *(1 + a) a*\/ polar_lift(c - a) c*\/ polar_lift(c - a) \ \/ a / \ \/ 1 + a /
----------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------
___________________________ ___________________ ___________________________ ___________________ ___________________________ ___________________ ___________________________ ___________________ ___________________________ ___________________ ___________________________ ___________________ 2 _______________________ ___________________ _______________________ ___________________ 2 _______________________ ___________________ _______________________ ___________________ ___________________________ ___________________ ___________________________ ___________________
a*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) - c*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) a*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) - c*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) a*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) - c*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) a *\/ a + polar_lift(c - a) *\/ polar_lift(c - a) - a*c*\/ a + polar_lift(c - a) *\/ polar_lift(c - a) a *\/ a + polar_lift(c - a) *\/ polar_lift(c - a) - a*c*\/ a + polar_lift(c - a) *\/ polar_lift(c - a) a*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a) - c*\/ 1 + a + polar_lift(c - a) *\/ polar_lift(c - a) *(1 + a)
$$\frac{a \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)}} \operatorname{asinh}{\left(\frac{\sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{\sqrt{a}} \right)}}{a^{2} \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)}} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - a c \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)}} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}} - \frac{a \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{a \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - c \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}} + \frac{c \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{a \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - c \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}} - \frac{c \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{a^{2} \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)}} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - a c \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)}} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}} - \frac{\left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \operatorname{asinh}{\left(\frac{\sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{\sqrt{a + 1}} \right)}}{a \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - c \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}} + \frac{\left(a + 1\right) \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}{a \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}} - c \left(a + 1\right) \sqrt{a + \operatorname{polar\_lift}{\left(- a + c \right)} + 1} \sqrt{\operatorname{polar\_lift}{\left(- a + c \right)}}}$$
c*sqrt(polar_lift(c - a))/(a*sqrt(1 + a + polar_lift(c - a))*sqrt(polar_lift(c - a))*(1 + a) - c*sqrt(1 + a + polar_lift(c - a))*sqrt(polar_lift(c - a))*(1 + a)) + sqrt(polar_lift(c - a))*(1 + a)/(a*sqrt(1 + a + polar_lift(c - a))*sqrt(polar_lift(c - a))*(1 + a) - c*sqrt(1 + a + polar_lift(c - a))*sqrt(polar_lift(c - a))*(1 + a)) - a*sqrt(polar_lift(c - a))/(a*sqrt(1 + a + polar_lift(c - a))*sqrt(polar_lift(c - a))*(1 + a) - c*sqrt(1 + a + polar_lift(c - a))*sqrt(polar_lift(c - a))*(1 + a)) - c*sqrt(polar_lift(c - a))/(a^2*sqrt(a + polar_lift(c - a))*sqrt(polar_lift(c - a)) - a*c*sqrt(a + polar_lift(c - a))*sqrt(polar_lift(c - a))) + a*sqrt(a + polar_lift(c - a))*asinh(sqrt(polar_lift(c - a))/sqrt(a))/(a^2*sqrt(a + polar_lift(c - a))*sqrt(polar_lift(c - a)) - a*c*sqrt(a + polar_lift(c - a))*sqrt(polar_lift(c - a))) - sqrt(1 + a + polar_lift(c - a))*(1 + a)*asinh(sqrt(polar_lift(c - a))/sqrt(1 + a))/(a*sqrt(1 + a + polar_lift(c - a))*sqrt(polar_lift(c - a))*(1 + a) - c*sqrt(1 + a + polar_lift(c - a))*sqrt(polar_lift(c - a))*(1 + a))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.