I try substituting u=sqrtx and ended up with the integral 2 * 0 to 1 u/(1+u)4 which would take too long multiplying it all out. What's the correct substitution?
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∫dx/(1 + √x)^4 from 0 to 1
u = 1 + √x
(u - 1)² = x
2(u - 1) du = dx
2*∫(u - 1)/(u^4) du from 1 to 2
2*∫(u^(-3) - u^(-4)) du from 1 to 2
= 2*[-1/2*u^(-2) + 1/3*u^(-3) eval. from 1 to 2]
= 2[-1/8 + 1/24 + 1/2 - 1/3]
= 1/6
u = 1 + √x
(u - 1)² = x
2(u - 1) du = dx
2*∫(u - 1)/(u^4) du from 1 to 2
2*∫(u^(-3) - u^(-4)) du from 1 to 2
= 2*[-1/2*u^(-2) + 1/3*u^(-3) eval. from 1 to 2]
= 2[-1/8 + 1/24 + 1/2 - 1/3]
= 1/6
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No need to expand. Write u/(u+1)^4 = [1/(u+1)^3 - 1/(u+1)^4] and then integrate.