不定积分最全公式

常见不定积分公式

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 d x=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 = -log

e |cos(x)|+C = log

e

|sec(x)|+C

5. ∫cot(x)dx = log e |sin(x)|+C

6. ∫sec(x)dx = log e |sec(x)+tan(x)|+C

7. ∫sin 2(x)dx

= 1 (x-sin(x)cos(x))+C 2

= 1 x - 1 sin(2x)+C 2 4

9. ∫cos 2(x)dx

= 1 (x+sin(x)cos(x))+C 2

= 1 x + 1 sin(2x)+C 2 4

11.∫tan 2(x)dx = tan(x)-x+C

12.∫cot 2(x)dx = -cot(x)-x+C

13.∫sin(ax)sin(bx)dx

= sin((a-b)x) - sin((a+b)x) +C 2(a-b) 2(a+b)

14.∫sin(ax)co s(bx)dx

= - cos((a-b)x) - cos((a+b)x) +C 2(a-b) 2(a+b)

15.∫cos(ax)cos(bx)dx

= sin((a-b)x) + sin((a+b)x) +C 2(a-b) 2(a+b)

16.∫xsin(x)dx = sin(x)-xcos(x)+C

17.∫xcos(x)dx = cos(x)+xsin(x)+C

18.∫x 2sin(x)dx = (2-x 2)cos(x)+2xsin(x)+C

19.∫x 2cos(x)dx = (x 2-2)sin(x)+2xcos(x)+C

20.∫e x dx = e x +C

21.

∫ a dx = a log |x| (a 为常数) x