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- La ecuación:
-
Ecuación x^2-4x+5=0
-
Ecuación x^2+3x+2=0
-
Ecuación x^2+3x=4
-
Ecuación -x^2+5*x-6=0
- Expresar {x} en función de y en la ecuación:
- 10*x-2*y=0
- 1*x+4*y=20
- 3*x-7*y=13
- 13*x-15*y=-6
- Integral de d{x}:
- lny
- Derivada de:
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lny
-
Expresiones idénticas
- lny=- dos ln(x^2+ uno)+const
- lny es igual a menos 2ln(x al cuadrado más 1) más const
- lny es igual a menos dos ln(x al cuadrado más uno) más const
- lny=-2ln(x2+1)+const
- lny=-2lnx2+1+const
- lny=-2ln(x²+1)+const
- lny=-2ln(x en el grado 2+1)+const
- lny=-2lnx^2+1+const
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Expresiones semejantes
- lny=+2ln(x^2+1)+const
- lny=-2ln(x^2-1)+const
- 0.5ln(y)=-ln(x+1)
- lny=-2ln(x^2+1)-const
- (y^2)-5y=log(y)+ln(y)
- x^2+5xy+y^2*ln(y/x)=0
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Expresiones con funciones
- lny
- lny=t
- lny=ax+by
- lny=(-1/x)+lnc
- lny+(x/y)^0.5=2
lny=-2ln(x^2+1)+const la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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/ 2 \ log(y) = - 2*log\x + 1/ + c
$$\log{\left(y \right)} = c - 2 \log{\left(x^{2} + 1 \right)}$$
Gráfica
Respuesta rápida
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/ / / c \ / c \\\ / / / c \ / c \\\
________________________________ | | | - | | - ||| ________________________________ | | | - | | - |||
/ 2 | | | 2 | | 2 ||| / 2 | | | 2 | | 2 |||
/ / / c \\ / c \ | | | e | | e ||| / / / c \\ / c \ | | | e | | e |||
/ | | - || | - | |atan2|im|-----|, -1 + re|-----||| / | | - || | - | |atan2|im|-----|, -1 + re|-----|||
/ | | 2 || | 2 | | | | ___| | ___||| / | | 2 || | 2 | | | | ___| | ___|||
/ | | e || 2| e | | \ \\/ y / \\/ y //| / | | e || 2| e | | \ \\/ y / \\/ y //|
x1 = - / |-1 + re|-----|| + im |-----| *cos|--------------------------------| - I* / |-1 + re|-----|| + im |-----| *sin|--------------------------------|
4 / | | ___|| | ___| \ 2 / 4 / | | ___|| | ___| \ 2 /
\/ \ \\/ y // \\/ y / \/ \ \\/ y // \\/ y /
$$x_{1} = - i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)}$$
/ / / c \ / c \\\ / / / c \ / c \\\
________________________________ | | | - | | - ||| ________________________________ | | | - | | - |||
/ 2 | | | 2 | | 2 ||| / 2 | | | 2 | | 2 |||
/ / / c \\ / c \ | | | e | | e ||| / / / c \\ / c \ | | | e | | e |||
/ | | - || | - | |atan2|im|-----|, -1 + re|-----||| / | | - || | - | |atan2|im|-----|, -1 + re|-----|||
/ | | 2 || | 2 | | | | ___| | ___||| / | | 2 || | 2 | | | | ___| | ___|||
/ | | e || 2| e | | \ \\/ y / \\/ y //| / | | e || 2| e | | \ \\/ y / \\/ y //|
x2 = / |-1 + re|-----|| + im |-----| *cos|--------------------------------| + I* / |-1 + re|-----|| + im |-----| *sin|--------------------------------|
4 / | | ___|| | ___| \ 2 / 4 / | | ___|| | ___| \ 2 /
\/ \ \\/ y // \\/ y / \/ \ \\/ y // \\/ y /
$$x_{2} = i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)}$$
x2 = i*((re(exp(c/2)/sqrt(y)) - 1)^2 + im(exp(c/2)/sqrt(y))^2)^(1/4)*sin(atan2(im(exp(c/2)/sqrt(y), re(exp(c/2)/sqrt(y)) - 1)/2) + ((re(exp(c/2)/sqrt(y)) - 1)^2 + im(exp(c/2)/sqrt(y))^2)^(1/4)*cos(atan2(im(exp(c/2)/sqrt(y)), re(exp(c/2)/sqrt(y)) - 1)/2))
Suma y producto de raíces
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suma
/ / / c \ / c \\\ / / / c \ / c \\\ / / / c \ / c \\\ / / / c \ / c \\\
________________________________ | | | - | | - ||| ________________________________ | | | - | | - ||| ________________________________ | | | - | | - ||| ________________________________ | | | - | | - |||
/ 2 | | | 2 | | 2 ||| / 2 | | | 2 | | 2 ||| / 2 | | | 2 | | 2 ||| / 2 | | | 2 | | 2 |||
/ / / c \\ / c \ | | | e | | e ||| / / / c \\ / c \ | | | e | | e ||| / / / c \\ / c \ | | | e | | e ||| / / / c \\ / c \ | | | e | | e |||
/ | | - || | - | |atan2|im|-----|, -1 + re|-----||| / | | - || | - | |atan2|im|-----|, -1 + re|-----||| / | | - || | - | |atan2|im|-----|, -1 + re|-----||| / | | - || | - | |atan2|im|-----|, -1 + re|-----|||
/ | | 2 || | 2 | | | | ___| | ___||| / | | 2 || | 2 | | | | ___| | ___||| / | | 2 || | 2 | | | | ___| | ___||| / | | 2 || | 2 | | | | ___| | ___|||
/ | | e || 2| e | | \ \\/ y / \\/ y //| / | | e || 2| e | | \ \\/ y / \\/ y //| / | | e || 2| e | | \ \\/ y / \\/ y //| / | | e || 2| e | | \ \\/ y / \\/ y //|
- / |-1 + re|-----|| + im |-----| *cos|--------------------------------| - I* / |-1 + re|-----|| + im |-----| *sin|--------------------------------| + / |-1 + re|-----|| + im |-----| *cos|--------------------------------| + I* / |-1 + re|-----|| + im |-----| *sin|--------------------------------|
4 / | | ___|| | ___| \ 2 / 4 / | | ___|| | ___| \ 2 / 4 / | | ___|| | ___| \ 2 / 4 / | | ___|| | ___| \ 2 /
\/ \ \\/ y // \\/ y / \/ \ \\/ y // \\/ y / \/ \ \\/ y // \\/ y / \/ \ \\/ y // \\/ y /
$$\left(- i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ / / / c \ / c \\\ / / / c \ / c \\\\ / / / / c \ / c \\\ / / / c \ / c \\\\ | ________________________________ | | | - | | - ||| ________________________________ | | | - | | - |||| | ________________________________ | | | - | | - ||| ________________________________ | | | - | | - |||| | / 2 | | | 2 | | 2 ||| / 2 | | | 2 | | 2 |||| | / 2 | | | 2 | | 2 ||| / 2 | | | 2 | | 2 |||| | / / / c \\ / c \ | | | e | | e ||| / / / c \\ / c \ | | | e | | e |||| | / / / c \\ / c \ | | | e | | e ||| / / / c \\ / c \ | | | e | | e |||| | / | | - || | - | |atan2|im|-----|, -1 + re|-----||| / | | - || | - | |atan2|im|-----|, -1 + re|-----|||| | / | | - || | - | |atan2|im|-----|, -1 + re|-----||| / | | - || | - | |atan2|im|-----|, -1 + re|-----|||| | / | | 2 || | 2 | | | | ___| | ___||| / | | 2 || | 2 | | | | ___| | ___|||| | / | | 2 || | 2 | | | | ___| | ___||| / | | 2 || | 2 | | | | ___| | ___|||| | / | | e || 2| e | | \ \\/ y / \\/ y //| / | | e || 2| e | | \ \\/ y / \\/ y //|| | / | | e || 2| e | | \ \\/ y / \\/ y //| / | | e || 2| e | | \ \\/ y / \\/ y //|| |- / |-1 + re|-----|| + im |-----| *cos|--------------------------------| - I* / |-1 + re|-----|| + im |-----| *sin|--------------------------------||*| / |-1 + re|-----|| + im |-----| *cos|--------------------------------| + I* / |-1 + re|-----|| + im |-----| *sin|--------------------------------|| | 4 / | | ___|| | ___| \ 2 / 4 / | | ___|| | ___| \ 2 /| |4 / | | ___|| | ___| \ 2 / 4 / | | ___|| | ___| \ 2 /| \ \/ \ \\/ y // \\/ y / \/ \ \\/ y // \\/ y / / \\/ \ \\/ y // \\/ y / \/ \ \\/ y // \\/ y / /
$$\left(- i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}{2} \right)}\right)$$
=
/ / c \ / c \\
________________________________ | | - | | - ||
/ 2 | | 2 | | 2 ||
/ / / c \\ / c \ | | e | | e ||
/ | | - || | - | I*atan2|im|-----|, -1 + re|-----||
/ | | 2 || | 2 | | | ___| | ___||
/ | | e || 2| e | \ \\/ y / \\/ y //
- / |-1 + re|-----|| + im |-----| *e
/ | | ___|| | ___|
\/ \ \\/ y // \\/ y /
$$- \sqrt{\left(\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)},\operatorname{re}{\left(\frac{e^{\frac{c}{2}}}{\sqrt{y}}\right)} - 1 \right)}}$$
-sqrt((-1 + re(exp(c/2)/sqrt(y)))^2 + im(exp(c/2)/sqrt(y))^2)*exp(i*atan2(im(exp(c/2)/sqrt(y)), -1 + re(exp(c/2)/sqrt(y))))