原式=∫(sin^2x+cos^2x)/(3sin^2x+4cos^2x)dx=∫(tan^2x+1)/(3tan^2x+4)dx=∫sec^2x/(3tan^2x+4)dx=∫1/(3tan^2x+4)dtanx=1/3∫1/(tan^2x+4/3)dtanx=1/3*1/(2/√3)arctan[tanx/(2/√3)]+C=1/(2√3)arctan[tanx/(2/√...