Sr Examen
Integral de sqrt(1+6/5*x^(1/5)) dx
Solución
Ha introducido
[src]
8 / | | _____________ | / 5 ___ | / 6*\/ x | / 1 + ------- dx | \/ 5 | / 0
$$\int\limits_{0}^{8} \sqrt{\frac{6 \sqrt[5]{x}}{5} + 1}\, dx$$
Integral(sqrt(1 + 6*x^(1/5)/5), (x, 0, 8))
Respuesta (Indefinida)
[src]
/ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ \ / | 6 31/5 29/5 32/5 28/5 33/5 27/5 34/5 26/5 7 5 ___ 5 / 5 ___ ___ 26/5 / 5 ___ ___ 8 / 5 ___ ___ 27/5 / 5 ___ ___ 28/5 / 5 ___ ___ 39/5 / 5 ___ ___ 29/5 / 5 ___ ___ 6 / 5 ___ ___ 31/5 / 5 ___ ___ 32/5 / 5 ___ ___ 38/5 / 5 ___ ___ 33/5 / 5 ___ ___ 37/5 / 5 ___ ___ 34/5 / 5 ___ ___ 36/5 / 5 ___ ___ 7 / 5 ___ | | ___ | 765450000000000*x 765450000000000*x 531562500000000*x 524880000000000*x 253125000000000*x 236196000000000*x 79101562500000*x 62985600000000*x 14648437500000*x 7558272000000*x 1220703125000*x 244140625000*\/ 5 *x *\/ 5 + 6*\/ x 2783203125000*\/ 5 *x *\/ 5 + 6*\/ x 9256766883840*\/ 5 *x *\/ 5 + 6*\/ x 14194335937500*\/ 5 *x *\/ 5 + 6*\/ x 42583007812500*\/ 5 *x *\/ 5 + 6*\/ x 77996832076800*\/ 5 *x *\/ 5 + 6*\/ x 83036865234375*\/ 5 *x *\/ 5 + 6*\/ x 111253183593750*\/ 5 *x *\/ 5 + 6*\/ x 118217601562500*\/ 5 *x *\/ 5 + 6*\/ x 163963490625000*\/ 5 *x *\/ 5 + 6*\/ x 295600238784000*\/ 5 *x *\/ 5 + 6*\/ x 354540037500000*\/ 5 *x *\/ 5 + 6*\/ x 663629508576000*\/ 5 *x *\/ 5 + 6*\/ x 696089295000000*\/ 5 *x *\/ 5 + 6*\/ x 977369600160000*\/ 5 *x *\/ 5 + 6*\/ x 987039464400000*\/ 5 *x *\/ 5 + 6*\/ x | | _____________ \/ 5 *|- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - 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--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | / 5 ___ | ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5 ___ 5 ___ 7 ___ 26/5 ___ 34/5 ___ 27/5 ___ 33/5 ___ 28/5 ___ 32/5 ___ 29/5 ___ 6 ___ 31/5| | / 6*\/ x \ 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x 1644521484375*\/ 5 *x + 10182443572224*\/ 5 *x + 19734257812500*\/ 5 *x + 84853696435200*\/ 5 *x + 106564992187500*\/ 5 *x + 318201361632000*\/ 5 *x + 341007975000000*\/ 5 *x + 707114136960000*\/ 5 *x + 716116747500000*\/ 5 *x + 1031208116400000*\/ 5 *x + 1031208116400000*\/ 5 *x / | / 1 + ------- dx = C + 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| \/ 5 5 | /
$$\int \sqrt{\frac{6 \sqrt[5]{x}}{5} + 1}\, dx = C + \frac{\sqrt{5} \left(\frac{77996832076800 \sqrt{5} x^{\frac{39}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{295600238784000 \sqrt{5} x^{\frac{38}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{663629508576000 \sqrt{5} x^{\frac{37}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{977369600160000 \sqrt{5} x^{\frac{36}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{696089295000000 \sqrt{5} x^{\frac{34}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} - \frac{62985600000000 x^{\frac{34}{5}}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{354540037500000 \sqrt{5} x^{\frac{33}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} - \frac{236196000000000 x^{\frac{33}{5}}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{163963490625000 \sqrt{5} x^{\frac{32}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} - \frac{524880000000000 x^{\frac{32}{5}}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{118217601562500 \sqrt{5} x^{\frac{31}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} - \frac{765450000000000 x^{\frac{31}{5}}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{83036865234375 \sqrt{5} x^{\frac{29}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} - \frac{531562500000000 x^{\frac{29}{5}}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{42583007812500 \sqrt{5} x^{\frac{28}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} - \frac{253125000000000 x^{\frac{28}{5}}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{14194335937500 \sqrt{5} x^{\frac{27}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} - \frac{79101562500000 x^{\frac{27}{5}}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{2783203125000 \sqrt{5} x^{\frac{26}{5}} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} - \frac{14648437500000 x^{\frac{26}{5}}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{9256766883840 \sqrt{5} x^{8} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{987039464400000 \sqrt{5} x^{7} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} - \frac{7558272000000 x^{7}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{111253183593750 \sqrt{5} x^{6} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} - \frac{765450000000000 x^{6}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} + \frac{244140625000 \sqrt{5} x^{5} \sqrt{6 \sqrt[5]{x} + 5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}} - \frac{1220703125000 x^{5}}{84853696435200 \sqrt{5} x^{\frac{34}{5}} + 318201361632000 \sqrt{5} x^{\frac{33}{5}} + 707114136960000 \sqrt{5} x^{\frac{32}{5}} + 1031208116400000 \sqrt{5} x^{\frac{31}{5}} + 716116747500000 \sqrt{5} x^{\frac{29}{5}} + 341007975000000 \sqrt{5} x^{\frac{28}{5}} + 106564992187500 \sqrt{5} x^{\frac{27}{5}} + 19734257812500 \sqrt{5} x^{\frac{26}{5}} + 10182443572224 \sqrt{5} x^{7} + 1031208116400000 \sqrt{5} x^{6} + 1644521484375 \sqrt{5} x^{5}}\right)}{5}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.