Integration shortcuts of [f(x)]^n also has derivative f'(x) (Integration Tips)
This integration trick can be applied when f(x) has a power n (here n ≠ 1) And derivate of f(x) is also persent of front of [f(x)]^n. Keep in mind always that n should not be equal to -1
In such case just take the f(x), take its power with plus 1 as power and divide by new power.
Let us we apply this integration rule on following examples.
Integration of x^2 or Integration of x raise to power 2
/ 2
| x dx
/
/ 2
= | x . 1 dx
/
(Here f(x) is x and 2 is its power, derivative of x is 1 which is also exist in front of x. So apply the above rule. Just take f(x), take its power with plus 1 as power and divide by new power.)
2 + 1
x
= ------- + C
2 + 1
3
x
= ----- + C
3
Integration of 1
/
| 1 dx
/
/ 0
= | x . dx
/
/ 0
= | x . 1 dx
/
(Here f(x) is x and 0 is its power, derivative of x is 1 which is also exist in front of x. So apply the above rule. Just take f(x), take its power with plus 1 as power and divide by new power.)
0 + 1
x
= ------- + C
0 + 1
1
x
= ----- + C
1
= x + C
Integration of (ln(x))/x
/
| ln(x)
| ----- dx
| x
/
/
| 1
= | ln(x) . --- dx
| x
/
(Here f(x) is ln(x) and 1 is its power, derivative of ln(x) is 1/x which is also exist in front of ln(x).So apply the above integration rule. Just take f(x), take its power with plus 1 as power and divide by new power.)
1 + 1
(ln(x))
= ------- + C
1 + 1
2
(ln x)
= ----- + C
2
Integration of (2x +3)^(1/2)
/
| 1/2
| (2x + 3) dx
/
/
1 | 1/2
= ---| (2x + 3) . 2 dx
2 |
/
(Here f(x) is 2x + 3 and 1/2 is its power, its derivative was not exit so we try to make its derivative by multiply and divided by 2. Now derivative of 2x + 3 is 2 which is in front of 2x + 3. So apply the above rule. Just take f(x), take its power with plus 1 as power and divide by new power.)
1
--- + 1
2
1 (2x + 3)
= --- -------- + C
2 1
--- + 1
2
3
---
2
1 (2x + 3)
= --- -------- + C
2 3
---
2
3/2
(2x + 3)
= --------
3
Integration Question
What is use of integration in our daily life ?
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What is integration of ZERO ?
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What is integration of C (constant) ?
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What is integration of 1 ?
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The power formula of int. use when ?
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Int. of x^n = x^(n+1)/n+1 is false when n = ?
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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)
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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)
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What is integration of 1/2x . Int (-2x) ? (-x, -2x, -x/2, -x^2/2)
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What is integration of (1+lnx)/xlnx ?
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What is integration of e^x ?
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What is integration of e^x = e^x/ ln e is true or false ?
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What is integration of e^-x ?
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What is integration of e^0 ?
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What is integration of e^1 ?
Integration Shortcuts (Solve in seconds)
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Integration shortcuts of [f(x)]^n also has derivative f'(x)
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Integration shortcuts of f(x) when f(x) is as denominator and has a derivative f΄(x) as nominator
Integration Worksheets with solution
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Integration Worksheets, Integration basics, Integration by parts, Integration by subtitutions with solution and downloadable.
CALCULAS Questions