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Integrate ∫ x8 (x9 - 10)5 dx by change of variable
Integrate ∫ x8 (x9 - 10)5 dx by change of variable.
Expert Solution
This question can be done by using change of variable method
integral is
∫ x8 (x9 - 10)5 dx
here, the best choice of variable is,
let
u = x9 - 10
du = 9 x8 dx
x8 dx = du/9 ( using substitution )
this integral can be written as : ∫ x8 (x9 - 10)5 dx = ∫ (( u )5 / 9 )du
(1/9) ∫ ( u )5 du
now we know that ∫ xn = xn+1 / n+1
= (1/9) * u6 / 6
=u6 / 54
= ( x9 - 10 )6 / 54
the answer of this indefinite integral will be ( x9 - 10 )6 / 54
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