不定积分最全公式.doc

常见不定常见不定积分公式积分公式 1）∫0dx=c 2）∫x^udx=(x^u+1)/(u+1)+c 3）∫1/xdx=ln|x|+c 4)）∫a^xdx=(a^x)/lna+c 5）∫e^xdx=e^x+c 6）∫sinxdx=-cosx+c 7）∫cosxdx=sinx+c 8）∫1/(cosx)^2dx=tanx+c 9）∫1/(sinx)^2dx=-cotx+c 10）∫1/√（1-x^2) dx=arcsinx+c 11）∫1/(1+x^2)dx=arctanx+c 12）∫1/(a^2-x^2)dx=(1/2a)ln|(a+x)/(a-x)|+c 13）∫secxdx=ln|secx+tanx|+c 14）∫1/(a^2+x^2)dx=1/a*arctan(x/a)+c 15）∫1/√(a^2-x^2) dx=arcsin(x/a)+c 16) ∫sec^2 x dx=tanx+c; 17) ∫shx dx=chx+c; 18) ∫chx dx=shx+c; 19) ∫thx dx=ln(chx)+c; 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 1 = 2 x - 4 sin(2x)+C 9. ∫cos2(x)dx 1 = 2 (x+sin(x)cos(x))+C 1 1 = 2 x + 4 sin(2x)+C 11.∫tan2(x)dx = tan(x)-x+C 12.∫cot2(x)dx = -cot(x)-x+C 13.∫sin(ax)sin(bx)dx sin((a-b)x) sin((a+b)x) = 2(a-b) - 2(a+b) +C 14.∫sin(ax)cos(bx)dx cos((a-b)x) cos((a+b)x) = - 2(a-b) - 2(a+b) +C 15.∫cos(ax)cos(bx)dx sin((a-b)x) sin((a+b)x) = 2(a-b) + 2(a+b) +C 16.∫xsin(x)dx = sin(x)-xcos(x)+C 17.∫xcos(x)dx = cos(x)+xsin(x)+C 18.∫x2sin(x)dx = (2-x2)cos(x)+2xsin(x)+C 19.∫x2cos(x)dx = (x2-2)sin(x)+2xcos(x)+C 20.∫exdx = ex+C 21.a ∫xdx = a log |x| (a 为常数)。