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Resolución de integrales/ 1/sqrt/ (4-x)/ 1/sqrt^8(4-x)^2

Integral de 1/sqrt^8(4-x)^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  6               
  /               
 |                
 |       1        
 |  ----------- dx
 |           64   
 |    _______     
 |  \/ 4 - x      
 |                
/                 
2
∫261(4−x)64 dx\int\limits_{2}^{6} \frac{1}{\left(\sqrt{4 - x}\right)^{64}}\, dx 
Integral(1/((sqrt(4 - x))^64), (x, 2, 6))
Solución detallada

  1. Hay varias maneras de calcular esta integral.

    Método #1

    1. Vuelva a escribir el integrando:

      1(4−x)64=1x32−128x31+7936x30−317440x29+9205760x28−206209024x27+3711762432x26−55146184704x25+689327308800x24−7352824627200x23+67645986570240x22−541167892561920x21+3788175247933440x20−23311847679590400x19+126550030260633600x18−607440145251041280x17+2581620617316925440x16−9719042324016660480x15+32396807746722201600x14−95485328095602278400x13+248261853048565923840x12−567455664111007825920x11+1134911328222015651840x10−1973758831690462003200x9+2960638247535693004800x8−3789616956845687046144x7+4081125953526124511232x6−3627667514245444009984x5+2591191081603888578560x4−1429622665712490250240x3+571849066284996100096x2−147573952589676412928x+18446744073709551616\frac{1}{\left(\sqrt{4 - x}\right)^{64}} = \frac{1}{x^{32} - 128 x^{31} + 7936 x^{30} - 317440 x^{29} + 9205760 x^{28} - 206209024 x^{27} + 3711762432 x^{26} - 55146184704 x^{25} + 689327308800 x^{24} - 7352824627200 x^{23} + 67645986570240 x^{22} - 541167892561920 x^{21} + 3788175247933440 x^{20} - 23311847679590400 x^{19} + 126550030260633600 x^{18} - 607440145251041280 x^{17} + 2581620617316925440 x^{16} - 9719042324016660480 x^{15} + 32396807746722201600 x^{14} - 95485328095602278400 x^{13} + 248261853048565923840 x^{12} - 567455664111007825920 x^{11} + 1134911328222015651840 x^{10} - 1973758831690462003200 x^{9} + 2960638247535693004800 x^{8} - 3789616956845687046144 x^{7} + 4081125953526124511232 x^{6} - 3627667514245444009984 x^{5} + 2591191081603888578560 x^{4} - 1429622665712490250240 x^{3} + 571849066284996100096 x^{2} - 147573952589676412928 x + 18446744073709551616}

    2. Vuelva a escribir el integrando:

      1x32−128x31+7936x30−317440x29+9205760x28−206209024x27+3711762432x26−55146184704x25+689327308800x24−7352824627200x23+67645986570240x22−541167892561920x21+3788175247933440x20−23311847679590400x19+126550030260633600x18−607440145251041280x17+2581620617316925440x16−9719042324016660480x15+32396807746722201600x14−95485328095602278400x13+248261853048565923840x12−567455664111007825920x11+1134911328222015651840x10−1973758831690462003200x9+2960638247535693004800x8−3789616956845687046144x7+4081125953526124511232x6−3627667514245444009984x5+2591191081603888578560x4−1429622665712490250240x3+571849066284996100096x2−147573952589676412928x+18446744073709551616=1(x−4)32\frac{1}{x^{32} - 128 x^{31} + 7936 x^{30} - 317440 x^{29} + 9205760 x^{28} - 206209024 x^{27} + 3711762432 x^{26} - 55146184704 x^{25} + 689327308800 x^{24} - 7352824627200 x^{23} + 67645986570240 x^{22} - 541167892561920 x^{21} + 3788175247933440 x^{20} - 23311847679590400 x^{19} + 126550030260633600 x^{18} - 607440145251041280 x^{17} + 2581620617316925440 x^{16} - 9719042324016660480 x^{15} + 32396807746722201600 x^{14} - 95485328095602278400 x^{13} + 248261853048565923840 x^{12} - 567455664111007825920 x^{11} + 1134911328222015651840 x^{10} - 1973758831690462003200 x^{9} + 2960638247535693004800 x^{8} - 3789616956845687046144 x^{7} + 4081125953526124511232 x^{6} - 3627667514245444009984 x^{5} + 2591191081603888578560 x^{4} - 1429622665712490250240 x^{3} + 571849066284996100096 x^{2} - 147573952589676412928 x + 18446744073709551616} = \frac{1}{\left(x - 4\right)^{32}}

    3. que u=x−4u = x - 4.

      Luego que du=dxdu = dx y ponemos dudu:

      ∫1u32 du\int \frac{1}{u^{32}}\, du

      1. Integral unu^{n} es un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫1u32 du=−131u31\int \frac{1}{u^{32}}\, du = - \frac{1}{31 u^{31}}

      Si ahora sustituir uu más en:

      −131(x−4)31- \frac{1}{31 \left(x - 4\right)^{31}}

    Método #2

    1. Vuelva a escribir el integrando:

      1(4−x)64=1x32−128x31+7936x30−317440x29+9205760x28−206209024x27+3711762432x26−55146184704x25+689327308800x24−7352824627200x23+67645986570240x22−541167892561920x21+3788175247933440x20−23311847679590400x19+126550030260633600x18−607440145251041280x17+2581620617316925440x16−9719042324016660480x15+32396807746722201600x14−95485328095602278400x13+248261853048565923840x12−567455664111007825920x11+1134911328222015651840x10−1973758831690462003200x9+2960638247535693004800x8−3789616956845687046144x7+4081125953526124511232x6−3627667514245444009984x5+2591191081603888578560x4−1429622665712490250240x3+571849066284996100096x2−147573952589676412928x+18446744073709551616\frac{1}{\left(\sqrt{4 - x}\right)^{64}} = \frac{1}{x^{32} - 128 x^{31} + 7936 x^{30} - 317440 x^{29} + 9205760 x^{28} - 206209024 x^{27} + 3711762432 x^{26} - 55146184704 x^{25} + 689327308800 x^{24} - 7352824627200 x^{23} + 67645986570240 x^{22} - 541167892561920 x^{21} + 3788175247933440 x^{20} - 23311847679590400 x^{19} + 126550030260633600 x^{18} - 607440145251041280 x^{17} + 2581620617316925440 x^{16} - 9719042324016660480 x^{15} + 32396807746722201600 x^{14} - 95485328095602278400 x^{13} + 248261853048565923840 x^{12} - 567455664111007825920 x^{11} + 1134911328222015651840 x^{10} - 1973758831690462003200 x^{9} + 2960638247535693004800 x^{8} - 3789616956845687046144 x^{7} + 4081125953526124511232 x^{6} - 3627667514245444009984 x^{5} + 2591191081603888578560 x^{4} - 1429622665712490250240 x^{3} + 571849066284996100096 x^{2} - 147573952589676412928 x + 18446744073709551616}

    2. Vuelva a escribir el integrando:

      1x32−128x31+7936x30−317440x29+9205760x28−206209024x27+3711762432x26−55146184704x25+689327308800x24−7352824627200x23+67645986570240x22−541167892561920x21+3788175247933440x20−23311847679590400x19+126550030260633600x18−607440145251041280x17+2581620617316925440x16−9719042324016660480x15+32396807746722201600x14−95485328095602278400x13+248261853048565923840x12−567455664111007825920x11+1134911328222015651840x10−1973758831690462003200x9+2960638247535693004800x8−3789616956845687046144x7+4081125953526124511232x6−3627667514245444009984x5+2591191081603888578560x4−1429622665712490250240x3+571849066284996100096x2−147573952589676412928x+18446744073709551616=1(x−4)32\frac{1}{x^{32} - 128 x^{31} + 7936 x^{30} - 317440 x^{29} + 9205760 x^{28} - 206209024 x^{27} + 3711762432 x^{26} - 55146184704 x^{25} + 689327308800 x^{24} - 7352824627200 x^{23} + 67645986570240 x^{22} - 541167892561920 x^{21} + 3788175247933440 x^{20} - 23311847679590400 x^{19} + 126550030260633600 x^{18} - 607440145251041280 x^{17} + 2581620617316925440 x^{16} - 9719042324016660480 x^{15} + 32396807746722201600 x^{14} - 95485328095602278400 x^{13} + 248261853048565923840 x^{12} - 567455664111007825920 x^{11} + 1134911328222015651840 x^{10} - 1973758831690462003200 x^{9} + 2960638247535693004800 x^{8} - 3789616956845687046144 x^{7} + 4081125953526124511232 x^{6} - 3627667514245444009984 x^{5} + 2591191081603888578560 x^{4} - 1429622665712490250240 x^{3} + 571849066284996100096 x^{2} - 147573952589676412928 x + 18446744073709551616} = \frac{1}{\left(x - 4\right)^{32}}

    3. que u=x−4u = x - 4.

      Luego que du=dxdu = dx y ponemos dudu:

      ∫1u32 du\int \frac{1}{u^{32}}\, du

      1. Integral unu^{n} es un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫1u32 du=−131u31\int \frac{1}{u^{32}}\, du = - \frac{1}{31 u^{31}}

      Si ahora sustituir uu más en:

      −131(x−4)31- \frac{1}{31 \left(x - 4\right)^{31}}

  2. Añadimos la constante de integración:

    −131(x−4)31+constant- \frac{1}{31 \left(x - 4\right)^{31}}+ \mathrm{constant}

Respuesta:

−131(x−4)31+constant- \frac{1}{31 \left(x - 4\right)^{31}}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
  /                                  
 |                                   
 |      1                     1      
 | ----------- dx = C - -------------
 |          64                     31
 |   _______            31*(-4 + x)  
 | \/ 4 - x                          
 |                                   
/
∫1(4−x)64 dx=C−131(x−4)31\int \frac{1}{\left(\sqrt{4 - x}\right)^{64}}\, dx = C - \frac{1}{31 \left(x - 4\right)^{31}}
Simplificar
Gráfica
2.06.02.53.03.54.04.55.05.52e72-1e72
Trazar el gráfico f(x)
Respuesta [src] 
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∞\infty 
=
= 
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∞\infty 
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    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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