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

1 Answer
Monzur R.
Feb 1, 2017

#int (5x^2-4)^7# #dx# #=(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=(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 (5x-4)^7# #dx# #=int78125 x^14 - 437500 x^12 + 1050000 x^10 - 1400000 x^8 + 1120000 x^6 - 537600 x^4 + 143360 x^2 - 16384#

#=(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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