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int(0)^( pi/2)(dx)/((4+9cos^(2)x))...

int_(0)^( pi/2)(dx)/((4+9cos^(2)x))

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int_0^(pi/2) (dx)/((4+9 cos^(2)x))

int_(0)^( pi)(x)/(4-cos^(2)x)dx

int_(0)^(pi//2)(1)/(4 cos^(2)x+9sin^(2)x)dx=

int_(0)^(pi) (x dx)/(4 cos^(2) x + 9 sin^(2) x)=

int_(0)^(pi)(x dx)/(4 cos^(2)x+9sin^(2)x)=

int_(0)^(pi)(x dx)/(4 cos^(2)x+9sin^(2)x)=

int_(0)^((pi)/(2))(1)/(4cos^(2)x+9sin^(2)x)dx=

int_(0)^(pi//2)(1)/(4cos^(2)x+9sin^(2)x)dx=

int_(0)^( pi/4)(1)/(cos^(2)x)dx

int_(0)^(pi//4)(dx)/((1+cos2x))