How do you use substitution to integrate #dx / (1− ( 8 x+4 ) ^2 )^ (1/2)#?

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Answer 1 · 2018-04-05T05:28:15

The answer is #=1/8arcsin(8x+4)+C#

Perform the substitution

#sintheta=8x+4#, #=>#, #costhetad theta=8dx#

#sqrt(1-(8s+4)^2)=sqrt(1-sin^2theta)=costheta#

Therefore, the integral is

#int(dx)/sqrt(1-(8x+4)^2)=1/8int(costheta d theta)/(cos theta)#

#=1/8theta#

#=1/8arcsin(8x+4)+C#