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# integration by subsitution watch

1. use the subsitution u = 4 + x^2
integral of x^3 / (4 + x^2)^1/2 with 1 at the top and zero at the bottom = 1/3(16 - 7 root 5)

du/dx = 2x
x=(u-4)^1/2
x=1, u=5
x=0, u =4

dx = du/2(u-4)^1/2

so integral ( 5 at top and 4 at bottom) = (u-4)^3/2 / (u)^1/2 . du/2(u-4)^1/2

from this i get

1/2 as a factor which ive taken out so i get the integral (5 at top and 5 at bottom)

u - 4 / (u)^1/2

if you integrate youd get something times ln u^1/2

struggling to find what the something is

2. Of course you can simplify the final answer to 1/3(16-7root5)
3. btw there is no In something for this integral unless your approach is different or you have made an error.

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