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Question Number 131147 by EDWIN88 last updated on 02/Feb/21

∫_( 0) ^( 1) ((3x^2 −1)/(1+(√(x−x^3 )))) dx =?

∫013x2−11+x−x3dx=?

Commented by EDWIN88 last updated on 02/Feb/21

(√(x−x^3 )) = w−1 ⇒x−x^3 =(w−1)^2 (1−3x^2 )dx=2(w−1)dw I=−∫_1 ^1 ((2w−1)/w) dw = ∫_1 ^( 1) ((1/w)−2)dw = [ ln ∣w∣−2w ]_1 ^1 = −2 −(−2) = 0

x−x3=w−1⇒x−x3=(w−1)2(1−3x2)dx=2(w−1)dwI=−∫112w−1wdw=∫11(1w−2)dw=[ln∣w∣−2w]11=−2−(−2)=0

Answered by Ar Brandon last updated on 02/Feb/21

Let u=x−x^3 then du=−(3x^2 −1)dx

Letu=x−x3thendu=−(3x2−1)dx

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