请给出∫cos^4(x)dx比我的解法更简洁方便的方法!∫cos^4(x)dx=1/8∫(cos2x+1)^2d2x=1/8∫[cos^2(2x)+2cos2x+1]d2x=1/8(sin4x/4+sin2x+3x)

Question

请给出∫cos^4(x)dx比我的解法更简洁方便的方法!
∫cos^4(x)dx =1/8∫(cos2x+1)^2d2x =1/8∫[cos^2(2x)+2cos2x+1]d2x =1/8(sin4x/4+sin2x+3x)

Answer 1

1.∫adx = ax+C (a 为常数) 2.∫sin(x)dx = -cos(x)+C 3.∫cos(x)dx = sin(x)+C 4.∫tan(x)dx = -loge|cos(x)|+C = loge|sec(x)|+C 5.∫cot(x)dx = loge|sin(x)|+C 6.∫sec(x)dx = loge|sec(x)+tan(x)|+C 7.∫sin2(x)dx =1/2(x-sin(x)cos(x))+C =1/2x -1/4sin(2x)+C 8.∫cos^2(x)dx =1/2(x+sin(x)cos(x))+C =1/2x +1/4sin(2x)+C 9.∫tan^2(x)dx = tan(x)-x+C 10.∫cot^2(x)dx = -cot(x)-x+C 11.∫sin(ax)sin(bx)dx =[sin((a-b)x) / 2(a-b)]-[sin((a+b)x) / 2(a+b)]+c 12.∫sin(ax)cos(bx)dx = -[cos((a-b)x) / 2(a-b)]-[cos((a+b)x) / 2(a+b)]+C 13.∫cos(ax)cos(bx)dx =[sin((a-b)x) / 2(a-b)]+[sin((a+b)x) / 2(a+b)]+C 14.∫xsin(x)dx = sin(x)-xcos(x)+C 15.∫xcos(x)dx = cos(x)+xsin(x)+C 16.∫x^2sin(x)dx = (2-x^2)cos(x)+2xsin(x)+C 17.∫x^2cos(x)dx = (x^2-2)sin(x)+2xcos(x)+C 18.∫e^xdx = e^x+C 19.∫a/xdx = a log |x| (a 为常数)