Question

how to integrate (5x^2-4)^7 ?

Answer 1

15625/ 3x^15 - 437500/13x^13 1050000/11x^11 -1400000/9x^9+160000x^7-107520x^5 + 143360/3x^3 - 16384x

Answer 2

That's what my calculator says. I pity the person who has to work this out by hand. I guess you'd just have to multiply and expand it all out and integrate each piece. Yikes!

Answer 3

oops left a plus out above
15625/ 3x^15 - 437500/13x^13 + 1050000/11x^11 -1400000/9x^9+160000x^7-107520x^5 + 143360/3x^3 - 16384x

Answer 4

Integration by parts didn't work out very well for me..
lemme try another method maybe.

Answer 5

@BangkokGarrett nope nope there is an easier an simpler way, but not your type of answer it's too long.

Answer 6

but i have no idea which way! :(

Answer 7

without expanding, I don't we can integrate it "compactly"

Answer 8

huhm... actually let me take back what I said. Perhaps, if we do
(5x^2-4)^7 = (sqrt(5)x - 2)^7 (sqrt(5)x + 2)^7, then integration by parts might work

Answer 9

thats what i meant! is there any answer?

Answer 10

well, let's try

u = (sqrt(5)x - 2)^7, dv = (sqrt(5)x + 2)^7

Answer 11

then,
du = 7sqrt(5) [sqrt(5)x - 2]^7, v = 1/[7sqrt(5)) (sqrt(5)x + 2]^8

is my math correct so far?

Answer 12

nope
du = 7sqrt(5) [sqrt(5)x - 2]^6, v = 1/[8sqrt(5)] (sqrt(5)x + 2]^8

Answer 13

(sqrt(5)x - 2)^7 * 1/[8sqrt(5)] (sqrt(5)x + 2]^8 - ∫ 7sqrt(5) [sqrt(5)x - 2]^7 * 1/[7sqrt(5)) (sqrt(5)x + 2]^8 dx

Answer 14

screw it XDD

Answer 15

@.@

Answer 16

haha never mind! I'll ask someone lol thanks for ur effort :)

Answer 17

expand using binomial theorem will certain faster than expanding using foil. But I don't see that's a really a simple way. Certainly the process is still tedious. Well, hello Wolfram Alpha lol