How do you evaluate #intsqrt(1-x^2)/sqrt(1-x)dx#?

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Answer 1 · 2018-07-18T14:39:27

#2/3(x+1)^{3/2}+C#

#\int \frac{\sqrt{1-x^2}}{\sqrt{1-x}}\ dx#

#=\int \frac{\sqrt{(1+x)(1-x)}}{\sqrt{1-x}}\ dx#

#=\int \sqrt{1+x}\ dx#

#=\int (x+1)^{1/2}\ dx#

#=\int (x+1)^{1/2}\ d(x+1)#

#=\frac{(x+1)^{1/2+1}}{1/2+1}+C#

#=2/3(x+1)^{3/2}+C#