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Resolución de integrales/ sin8x/ sin^4/ sin8x/9+sin^44x

Integral de sin8x/9+sin^44x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                         
  /                         
 |                          
 |  /sin(8*x)      44   \   
 |  |-------- + sin  (x)| dx
 |  \   9               /   
 |                          
/                           
0
∫01(sin⁡44(x)+sin⁡(8x)9) dx\int\limits_{0}^{1} \left(\sin^{44}{\left(x \right)} + \frac{\sin{\left(8 x \right)}}{9}\right)\, dx 
Integral(sin(8*x)/9 + sin(x)^44, (x, 0, 1))
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.25-0.25
Trazar el gráfico f(x)
Respuesta [src] 
                                                                      3                            11                            7                            5                            9                           13                           21                           19                           15                           17                          27                          23                          25                         29                       31                       33                       35                      37                     39                   41                43          
2641989241129    cos(8)   263012370465*cos(1)*sin(1)   87670790155*sin (1)*cos(1)   87670790155*sin  (1)*cos(1)   52602474093*sin (1)*cos(1)   17534158031*sin (1)*cos(1)   17534158031*sin (1)*cos(1)   6743906935*sin  (1)*cos(1)   6743906935*sin  (1)*cos(1)   4046344161*sin  (1)*cos(1)   1348781387*sin  (1)*cos(1)   1348781387*sin  (1)*cos(1)   762354697*sin  (1)*cos(1)   293213345*sin  (1)*cos(1)   175928007*sin  (1)*cos(1)   26288093*sin  (1)*cos(1)   848003*sin  (1)*cos(1)   848003*sin  (1)*cos(1)   848003*sin  (1)*cos(1)   22919*sin  (1)*cos(1)   1763*sin  (1)*cos(1)   43*sin  (1)*cos(1)   sin  (1)*cos(1)
-------------- - ------ - -------------------------- - -------------------------- - --------------------------- - -------------------------- - -------------------------- - -------------------------- - -------------------------- - -------------------------- - -------------------------- - -------------------------- - -------------------------- - ------------------------- - ------------------------- - ------------------------- - ------------------------ - ---------------------- - ---------------------- - ---------------------- - --------------------- - -------------------- - ------------------ - ---------------
19791209299968     72           2199023255552                1099511627776                 1984274890752                 962072674304                 274877906944                 360777252864                 165356240896                 208633069568                 119218896896                 35433480192                  37648072704                  26671841280                  9483321344                  5927075840                 952565760                  31752192                 32744448                 33707520                  936320                 73920                  1848                 44
−263012370465sin⁡(1)cos⁡(1)2199023255552−87670790155sin⁡3(1)cos⁡(1)1099511627776−17534158031sin⁡5(1)cos⁡(1)274877906944−52602474093sin⁡7(1)cos⁡(1)962072674304−17534158031sin⁡9(1)cos⁡(1)360777252864−87670790155sin⁡11(1)cos⁡(1)1984274890752−6743906935sin⁡13(1)cos⁡(1)165356240896−1348781387sin⁡15(1)cos⁡(1)35433480192−1348781387sin⁡17(1)cos⁡(1)37648072704−4046344161sin⁡19(1)cos⁡(1)119218896896−6743906935sin⁡21(1)cos⁡(1)208633069568−293213345sin⁡23(1)cos⁡(1)9483321344−175928007sin⁡25(1)cos⁡(1)5927075840−762354697sin⁡27(1)cos⁡(1)26671841280−26288093sin⁡29(1)cos⁡(1)952565760−848003sin⁡31(1)cos⁡(1)31752192−848003sin⁡33(1)cos⁡(1)32744448−848003sin⁡35(1)cos⁡(1)33707520−22919sin⁡37(1)cos⁡(1)936320−1763sin⁡39(1)cos⁡(1)73920−43sin⁡41(1)cos⁡(1)1848−sin⁡43(1)cos⁡(1)44−cos⁡(8)72+264198924112919791209299968- \frac{263012370465 \sin{\left(1 \right)} \cos{\left(1 \right)}}{2199023255552} - \frac{87670790155 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{1099511627776} - \frac{17534158031 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{274877906944} - \frac{52602474093 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{962072674304} - \frac{17534158031 \sin^{9}{\left(1 \right)} \cos{\left(1 \right)}}{360777252864} - \frac{87670790155 \sin^{11}{\left(1 \right)} \cos{\left(1 \right)}}{1984274890752} - \frac{6743906935 \sin^{13}{\left(1 \right)} \cos{\left(1 \right)}}{165356240896} - \frac{1348781387 \sin^{15}{\left(1 \right)} \cos{\left(1 \right)}}{35433480192} - \frac{1348781387 \sin^{17}{\left(1 \right)} \cos{\left(1 \right)}}{37648072704} - \frac{4046344161 \sin^{19}{\left(1 \right)} \cos{\left(1 \right)}}{119218896896} - \frac{6743906935 \sin^{21}{\left(1 \right)} \cos{\left(1 \right)}}{208633069568} - \frac{293213345 \sin^{23}{\left(1 \right)} \cos{\left(1 \right)}}{9483321344} - \frac{175928007 \sin^{25}{\left(1 \right)} \cos{\left(1 \right)}}{5927075840} - \frac{762354697 \sin^{27}{\left(1 \right)} \cos{\left(1 \right)}}{26671841280} - \frac{26288093 \sin^{29}{\left(1 \right)} \cos{\left(1 \right)}}{952565760} - \frac{848003 \sin^{31}{\left(1 \right)} \cos{\left(1 \right)}}{31752192} - \frac{848003 \sin^{33}{\left(1 \right)} \cos{\left(1 \right)}}{32744448} - \frac{848003 \sin^{35}{\left(1 \right)} \cos{\left(1 \right)}}{33707520} - \frac{22919 \sin^{37}{\left(1 \right)} \cos{\left(1 \right)}}{936320} - \frac{1763 \sin^{39}{\left(1 \right)} \cos{\left(1 \right)}}{73920} - \frac{43 \sin^{41}{\left(1 \right)} \cos{\left(1 \right)}}{1848} - \frac{\sin^{43}{\left(1 \right)} \cos{\left(1 \right)}}{44} - \frac{\cos{\left(8 \right)}}{72} + \frac{2641989241129}{19791209299968} 
=
= 
                                                                      3                            11                            7                            5                            9                           13                           21                           19                           15                           17                          27                          23                          25                         29                       31                       33                       35                      37                     39                   41                43          
2641989241129    cos(8)   263012370465*cos(1)*sin(1)   87670790155*sin (1)*cos(1)   87670790155*sin  (1)*cos(1)   52602474093*sin (1)*cos(1)   17534158031*sin (1)*cos(1)   17534158031*sin (1)*cos(1)   6743906935*sin  (1)*cos(1)   6743906935*sin  (1)*cos(1)   4046344161*sin  (1)*cos(1)   1348781387*sin  (1)*cos(1)   1348781387*sin  (1)*cos(1)   762354697*sin  (1)*cos(1)   293213345*sin  (1)*cos(1)   175928007*sin  (1)*cos(1)   26288093*sin  (1)*cos(1)   848003*sin  (1)*cos(1)   848003*sin  (1)*cos(1)   848003*sin  (1)*cos(1)   22919*sin  (1)*cos(1)   1763*sin  (1)*cos(1)   43*sin  (1)*cos(1)   sin  (1)*cos(1)
-------------- - ------ - -------------------------- - -------------------------- - --------------------------- - -------------------------- - -------------------------- - -------------------------- - -------------------------- - -------------------------- - -------------------------- - -------------------------- - -------------------------- - ------------------------- - ------------------------- - ------------------------- - ------------------------ - ---------------------- - ---------------------- - ---------------------- - --------------------- - -------------------- - ------------------ - ---------------
19791209299968     72           2199023255552                1099511627776                 1984274890752                 962072674304                 274877906944                 360777252864                 165356240896                 208633069568                 119218896896                 35433480192                  37648072704                  26671841280                  9483321344                  5927075840                 952565760                  31752192                 32744448                 33707520                  936320                 73920                  1848                 44
−263012370465sin⁡(1)cos⁡(1)2199023255552−87670790155sin⁡3(1)cos⁡(1)1099511627776−17534158031sin⁡5(1)cos⁡(1)274877906944−52602474093sin⁡7(1)cos⁡(1)962072674304−17534158031sin⁡9(1)cos⁡(1)360777252864−87670790155sin⁡11(1)cos⁡(1)1984274890752−6743906935sin⁡13(1)cos⁡(1)165356240896−1348781387sin⁡15(1)cos⁡(1)35433480192−1348781387sin⁡17(1)cos⁡(1)37648072704−4046344161sin⁡19(1)cos⁡(1)119218896896−6743906935sin⁡21(1)cos⁡(1)208633069568−293213345sin⁡23(1)cos⁡(1)9483321344−175928007sin⁡25(1)cos⁡(1)5927075840−762354697sin⁡27(1)cos⁡(1)26671841280−26288093sin⁡29(1)cos⁡(1)952565760−848003sin⁡31(1)cos⁡(1)31752192−848003sin⁡33(1)cos⁡(1)32744448−848003sin⁡35(1)cos⁡(1)33707520−22919sin⁡37(1)cos⁡(1)936320−1763sin⁡39(1)cos⁡(1)73920−43sin⁡41(1)cos⁡(1)1848−sin⁡43(1)cos⁡(1)44−cos⁡(8)72+264198924112919791209299968- \frac{263012370465 \sin{\left(1 \right)} \cos{\left(1 \right)}}{2199023255552} - \frac{87670790155 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{1099511627776} - \frac{17534158031 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{274877906944} - \frac{52602474093 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{962072674304} - \frac{17534158031 \sin^{9}{\left(1 \right)} \cos{\left(1 \right)}}{360777252864} - \frac{87670790155 \sin^{11}{\left(1 \right)} \cos{\left(1 \right)}}{1984274890752} - \frac{6743906935 \sin^{13}{\left(1 \right)} \cos{\left(1 \right)}}{165356240896} - \frac{1348781387 \sin^{15}{\left(1 \right)} \cos{\left(1 \right)}}{35433480192} - \frac{1348781387 \sin^{17}{\left(1 \right)} \cos{\left(1 \right)}}{37648072704} - \frac{4046344161 \sin^{19}{\left(1 \right)} \cos{\left(1 \right)}}{119218896896} - \frac{6743906935 \sin^{21}{\left(1 \right)} \cos{\left(1 \right)}}{208633069568} - \frac{293213345 \sin^{23}{\left(1 \right)} \cos{\left(1 \right)}}{9483321344} - \frac{175928007 \sin^{25}{\left(1 \right)} \cos{\left(1 \right)}}{5927075840} - \frac{762354697 \sin^{27}{\left(1 \right)} \cos{\left(1 \right)}}{26671841280} - \frac{26288093 \sin^{29}{\left(1 \right)} \cos{\left(1 \right)}}{952565760} - \frac{848003 \sin^{31}{\left(1 \right)} \cos{\left(1 \right)}}{31752192} - \frac{848003 \sin^{33}{\left(1 \right)} \cos{\left(1 \right)}}{32744448} - \frac{848003 \sin^{35}{\left(1 \right)} \cos{\left(1 \right)}}{33707520} - \frac{22919 \sin^{37}{\left(1 \right)} \cos{\left(1 \right)}}{936320} - \frac{1763 \sin^{39}{\left(1 \right)} \cos{\left(1 \right)}}{73920} - \frac{43 \sin^{41}{\left(1 \right)} \cos{\left(1 \right)}}{1848} - \frac{\sin^{43}{\left(1 \right)} \cos{\left(1 \right)}}{44} - \frac{\cos{\left(8 \right)}}{72} + \frac{2641989241129}{19791209299968} 
2641989241129/19791209299968 - cos(8)/72 - 263012370465*cos(1)*sin(1)/2199023255552 - 87670790155*sin(1)^3*cos(1)/1099511627776 - 87670790155*sin(1)^11*cos(1)/1984274890752 - 52602474093*sin(1)^7*cos(1)/962072674304 - 17534158031*sin(1)^5*cos(1)/274877906944 - 17534158031*sin(1)^9*cos(1)/360777252864 - 6743906935*sin(1)^13*cos(1)/165356240896 - 6743906935*sin(1)^21*cos(1)/208633069568 - 4046344161*sin(1)^19*cos(1)/119218896896 - 1348781387*sin(1)^15*cos(1)/35433480192 - 1348781387*sin(1)^17*cos(1)/37648072704 - 762354697*sin(1)^27*cos(1)/26671841280 - 293213345*sin(1)^23*cos(1)/9483321344 - 175928007*sin(1)^25*cos(1)/5927075840 - 26288093*sin(1)^29*cos(1)/952565760 - 848003*sin(1)^31*cos(1)/31752192 - 848003*sin(1)^33*cos(1)/32744448 - 848003*sin(1)^35*cos(1)/33707520 - 22919*sin(1)^37*cos(1)/936320 - 1763*sin(1)^39*cos(1)/73920 - 43*sin(1)^41*cos(1)/1848 - sin(1)^43*cos(1)/44
Respuesta numérica [src] 
0.0159263476338071
0.0159263476338071

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