- #1

Crystal037

- 165

- 7

- Homework Statement:
- Integrate 1/(x(1-x))^(1/2)dx

- Relevant Equations:
- Integral of 1/rt(1-x^2)dx = arcsinx

Let x=t^2

Then dx=2t dt

Integral of 1/(x(1-x))^(1/2)dx

= integral of 2tdt/t(1-t^2) ^(1/2)

= integral of 2dt/(1-t^2) ^(1/2)

= 2 arcsin(t) +c

= 2 arcsin(rt(x)) +c.

But the answer in my book is arcsin(2x-1) +c.

Tell me how

2 arcsin(rt(x) +C= arcsin(2x-1) +c

I know the constant will vary for both the answers and both the answers must come equal after some manipulation. Is my answer correct.

Then dx=2t dt

Integral of 1/(x(1-x))^(1/2)dx

= integral of 2tdt/t(1-t^2) ^(1/2)

= integral of 2dt/(1-t^2) ^(1/2)

= 2 arcsin(t) +c

= 2 arcsin(rt(x)) +c.

But the answer in my book is arcsin(2x-1) +c.

Tell me how

2 arcsin(rt(x) +C= arcsin(2x-1) +c

I know the constant will vary for both the answers and both the answers must come equal after some manipulation. Is my answer correct.