plz help show me steps solution
evaluate the integral
§dx/[(x+1)root(1-x^2)]
∫dx/((x+1)√(1-x^2))
I'd try a trig substitution on this one
x = sinu
dx = cosu du
√(1-x^2) = cosu
Now you have
∫(cosu du)/((1+sinu)cosu)
= ∫1/(1+sinu) du
= ∫(1-sinu)/(1-sin^2u) du
= ∫(1-sinu)/cos^2u du
= ∫sec^2u du - ∫secu tanu du
= tanu - secu
= (sinu-1)/cosu
= (x-1)/√(1-x^2) + C
I didn't get very far trying to manipulate the √(1-x^2) directly.