- #1
Agent M27
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- 0
Homework Statement
[tex]\int\frac{dx}{\sqrt{x}\sqrt{1-x}}[/tex]
Homework Equations
[tex]\int\frac{du}{\sqrt{a^{2}-u^{2}}}= arcsin\frac{u}{a} + C[/tex]
The Attempt at a Solution
u[tex]^{2}[/tex]=x
dx=2u du
[tex]\int\frac{2u}{u\sqrt{1-u^{2}}}du[/tex]
2[tex]\int\frac{du}{\sqrt{1-u^{2}}} = 2arcsin\frac{u}{a} + C[/tex]
=2arcsin([tex]\sqrt{x}[/tex]) + C
But the book gives the answer to be 2arcsec([tex]\sqrt{x}[/tex]) + C, which I do not understand how they achieved that answer. Any help would be appreciated. Thank you.
Joe