How do you integrate $y = {(5 x^{2} - 4)}^{7}$ $y=(5x^2 - 4)^7$ ?

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How do you integrate $y = {(5 x^{2} - 4)}^{7}$ $y=(5x^2 - 4)^7$ ?

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Answer 1 · 2017-02-01T23:40:03

$\int {(5 x^{2} - 4)}^{7}$ $int (5x^2-4)^7$ $d x$ $dx$ $= \frac{15625 x^{15}}{3} - \frac{437500 x^{13}}{13} + \frac{1050000 x^{11}}{11} - \frac{1400000 x^{9}}{9} + 160000 x^{7} - 107520 x^{5} + \frac{143360 x^{3}}{3} - 16384 x + c$ $=(15625 x^15)/3 - (437500 x^13)/13 + (1050000 x^11)/11 - (1400000 x^9)/9 + 160000 x^7 - 107520 x^5 + (143360 x^3)/3 - 16384 x + "c"$

Explanation:

$y = {(5 x^{2} - 4)}^{7} = 78125 x^{14} - 437500 x^{12} + 1050000 x^{10} - 1400000 x^{8} + 1120000 x^{6} - 537600 x^{4} + 143360 x^{2} - 16384$ $y=(5x^2-4)^7=78125 x^14 - 437500 x^12 + 1050000 x^10 - 1400000 x^8 + 1120000 x^6 - 537600 x^4 + 143360 x^2 - 16384$

$\int {(5 x - 4)}^{7}$ $int (5x-4)^7$ $d x$ $dx$ $= \int 78125 x^{14} - 437500 x^{12} + 1050000 x^{10} - 1400000 x^{8} + 1120000 x^{6} - 537600 x^{4} + 143360 x^{2} - 16384$ $=int78125 x^14 - 437500 x^12 + 1050000 x^10 - 1400000 x^8 + 1120000 x^6 - 537600 x^4 + 143360 x^2 - 16384$

$= \frac{15625 x^{15}}{3} - \frac{437500 x^{13}}{13} + \frac{1050000 x^{11}}{11} - \frac{1400000 x^{9}}{9} + 160000 x^{7} - 107520 x^{5} + \frac{143360 x^{3}}{3} - 16384 x + c$ $=(15625 x^15)/3 - (437500 x^13)/13 + (1050000 x^11)/11 - (1400000 x^9)/9 + 160000 x^7 - 107520 x^5 + (143360 x^3)/3 - 16384 x + "c"$

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How do you integrate $y = {(5 x^{2} - 4)}^{7}$ $y=(5x^2 - 4)^7$ ?

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How do you integrate y=(5x2−4)7 y=(5x^2 - 4)^7?

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How do you integrate $y = {(5 x^{2} - 4)}^{7}$ $y=(5x^2 - 4)^7$ ?