Integrating x(1-x)^1/2: A Calculus Headache Solved

[Jbreezy]

Homework Statement

Hey I'm doing something really stupid it is really pissing me off why I can't figure it out.

The Attempt at a Solution

Evaulate the integral : ∫ x(1-x)^1/2

I tried with substitution. u = 1-x , -du = dx and x = 1-u

∫ (1-u)(u)^1/2 I just tried to simplify it some.

∫ (u^1/2-u^3/2) -du

-∫ u^1/2 du +∫ u^3/2 du

integrate I got

(-2/3)u^ 3/2 + (2/5)u^5/2


(-2/3)(1-x)^ 3/2 + (2/5)(1-x)^5/2


My book got (-2/15)*2+3x)(1-x)^3/2 + C
I'm lost.

Thanks for the help.

 

[Mark44]

Homework Statement

Hey I'm doing something really stupid it is really pissing me off why I can't figure it out.

The Attempt at a Solution

Evaulate the integral : ∫ x(1-x)^1/2

I tried with substitution. u = 1-x , -du = dx and x = 1-u

∫ (1-u)(u)^1/2 I just tried to simplify it some.

∫ (u^1/2-u^3/2) -du

-∫ u^1/2 du +∫ u^3/2 du

integrate I got

(-2/3)u^ 3/2 + (2/5)u^5/2


(-2/3)(1-x)^ 3/2 + (2/5)(1-x)^5/2


My book got (-2/15)*2+3x)(1-x)^3/2 + C
I'm lost.

Thanks for the help.

It looks to me like they factored (1 - x)^3/2 from both terms.

 

[Jbreezy]

I just tried that and couldn't get it in the form they had.

 

[Jbreezy]

I think I just got it sorry. Jesus this was mad so much harder by me ..Thanks for help