INTEGRATION TRICKS IN 2 SEC FOR CBSE / JEE / IIT JEE / JEE MAIN / NDA /JEE ADVANCED/WBJEE

– Hello students I am Bijoy and welcome to our educational forum. Today we will know about the integration formula and at the we will download formula list in pdf file.

Introduction:

First you have to know that what is integration? In previous class we uploaded the Integration tutorials you can views that. In generally there have two types of formula that’s are (A) fundamental formula and (B) some standard form on integrals. But some where you can see formula divide on the basis of function like algebraic function, trigonometric function, exponential function etc. it depends upon the different teachers.

Let’s see the Formula list

(A) Fundamental Integrals :

1) ∫ Af(x) dx = A ∫ f(x) dx

2) ∫ dx = x + c

3) ∫ xn dx = ​$$\frac {x^(n+1)}{n+1}$$​ +c ;  ( n≠1)

4) ∫ emx dx = ​$$\frac{e^(mx)}{m}$$​ + c

5) ∫ (1/x) dx = log|x| + c

6) ∫ ex dx = ex + c

7) ∫ amx dx = amx / mlog|a|  + c  ( a≠1)

8) ∫ ax dx = ax /log|a\ + c

9) ∫ sinmx dx = ​$$– \frac {cosmx}{m}$$​ + c

10) ∫ sinx dx = – cosx + c

11) ∫ cosmx dx = ​$$\frac {sinmx}{m}$$​ + c

12) ∫ cosx dx = sinx + c

13) ∫ sec2mx dx = ​$$\frac {tanmx}{m}$$​ + c

14) ∫ sec2 x dx = tanx + c

15) ∫ cosec2mx dx = ​$$– \frac {cotmx}{m}$$​ + c

16) ∫ cosec2x dx = – cotx + c

17) ∫ secmx · tanmx dx = ​$$\frac{secmx}{m}$$​ + c

18) ∫ secx · tanx dx = secx + c

19) ∫ cosecmx · cotmx dx = ​​$$– \frac {cosecmx}{m}$$​ + c

20) ∫ cosecx · cotx dx  = – cosecx + c

# Some important forms of Integrals :

21) If n≠ -1 then, ∫ {f(x)}n · f(x) dx = (1/n+1) × {f(x)}n+1 + c

22) ∫ f(x)/f(x) dx = log|f(x)| + c

23) ∫ ex [ f(x) + f(x) ] dx = ex·f(x) + c

24) ∫ tanx dx = log|secx| + c

25) ∫ cotx dx = log|sinx| + c

26) ∫ secx dx = log| secx + tanx | + c

27) cosecx dx = log | cosecx – cotx | + c

(B) Some Standard Integrals:

35) ∫ eax· sinbx dx = ​$$\frac{e^(ax)}{a^2+b^2}$$​ ( asinbx – bcosbx ) + c

36) ∫ eax· cosbx dx = ​$$\frac {e^(ax)}{a^2+b^2}$$​ (a cosbx + b sinbx ) + c

SUMMATION SERIES INTEGRATION SHORTCUT FOR CBSE/JEE MAIN/JEE ADVANCED/IIT JEE/NTA/NDA