April 18, 2016

what is the integral of (1-x)^(1/3)?

what is the integral of (1-x)^(1/3)?

Comments

poo6473

Let u = 1-x and du = -dx

Then you have

Integral – u^(1/3) du

= [-u^4/3] / (4/3) +C

= [-3u^(4/3)]/4 + C

= [-3 * (1-x)^(4/3)]/4 + C

redbelle

(x-x^2)^4/3 + c

peace w

u=1-x
du=-1
(u)^4/3/(4/3)
3/4(1-x)^4/3+c

nelly212002

Integration by substitution is not required or this integral, just integrate using the power rule then divide by the derivative of the bracket.

? ³?(1 – x) dx = -3[³?(1 – x)?] / 4 + C
? ³?(1 – x) dx = C – 3[³?(x – 1)?] / 4

piano_chic03

? (1 – x)^(1/3) dx

Let u = 1 – x, so by differentiation:

du/dx = -1
du = -dx
-du = dx

This gives us:

-? u^(1/3) du

Finally, by power rule ? x? dx = x^(n + 1)/(n + 1) + c…

-u^(1/3 + 1)/(1/3 + 1) + c
= -u^(1/3 + 3/3)/(1/3 + 3/3) + c
= -u^(4/3)/(4/3) + c
= -3u^(4/3)/4 + c
= -3(1 – x)^(4/3)/4 + c

I hope this helps!

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