[" 8."int(dx)/(x(1+x^(2)))],[|C|sin2012|]

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" (8) "int(sin x)/(cos^(2)x)dx

int(sin2x)/(1+sin^(2)x)dx=

int(cos x)/((1+sin x)(2+sin x))dx

int(cos x)/((1-sin x)(2-sin x))dx

int(dx)/(sqrt(a^(2)-x^(2)))=sin^(-1)(x/a)+C

If int(x)/(sqrt(8-2x-x^(2)))dx=a sin^(-1)((x+1)/(3))+b sqrt(8-2x-x^(2))+c , then

int(1)/(1+sin2x+sin^(2)x)dx=

int (sin^-1x)/x^2 dx