Integration of e^x = ...?
---- + C
We know the integration formula of "a raise to power x".
| x a
| a dx = ------ + C for base 10 logarithm .....(i)
| log a
Similarly for "e raise to power x".
| x e
| e dx = ------ + C for base e logarithm ..... (ii)
| ln e
We should memorize the formulas (i) & (ii) because it is easy to remember, clear the basic concept and theam of boths result are also same.
Here because ln e = 1 (because e^0 = 1 and by use logarithm property we get ln e = 1 ) after simplification we can get
= ------ = ------ = e^x
ln e 1
/ x x
| e dx = e + C ......... (iii)
Integration formulas (ii) & (iii) are same formula. We mostly use formula (iii) because it is understood that "ln e = 1". Just keep in mind the original formula (ii) and there is also the hidden knownledge that "ln e = 1".
| x e
| e dx = ------ + C (here ln e = 1)
| ln e
What is use of integration in our daily life ?
What is integration of ZERO ?
What is integration of C (constant) ?
What is integration of 1 ?
The power formula of int. use when ?
Int. of x^n = x^(n+1)/n+1 is false when n = ?
Int. of x^0.1 = ?
(x^0.1/0.1, x^0.2/0.2, x^1.1/1.1, x^2.2/2.2)
Int. of x^0.07 = ? (x^0.8/0.8, x^0.08/0.08, x^0.17/0.17, x^1.07/1.07)
What is integration of 1/2x . Int (-2x) ? (-x, -2x, -x/2, -x^2/2)
What is integration of (1+lnx)/xlnx ?
What is integration of e^x ?
What is integration of e^x = e^x/ ln e is true or false ?
What is integration of e^-x ?
What is integration of e^0 ?
What is integration of e^1 ?
Integration Shortcuts (Solve in seconds)
Integration shortcuts of [f(x)]^n also has derivative f'(x)
Integration shortcuts of f(x) when f(x) is as denominator and has a derivative f΄(x) as nominator
Integration Worksheets with solution
Integration Worksheets, Integration basics, Integration by parts, Integration by subtitutions with solution and downloadable.