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| Integrate(CAS
mode) |
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| Integrates
an expression. |
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[F2](CALC)[2]( ) |
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( expression , var , lower , upper [ ,
constant of integration ] [ ) ]
( expression [ , var ] [ ) ]
( expression , var [ , constant if integration
] [ ) ] |
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| 1. |
To
integrate X^2 with respect to X.
[F2](CALC)[2]( )[X][X^2][EXE]
|
|
| 2. |
( X ln(X), X ) |
X2
ln(X)/2 - X2/4 |
| 3. |
( sin(AX), X, 2, 1 ) |
-cos(A)/A
+ cos(2A)/A |
| 4. |
( X, X, A, B ) |
-A2/2
+ B2/2 |
| 5. |
( X e (-X2+1), X, 0, 
) |
e/2 |
| 6. |
( 1/(X ln(X)), X, 1, 2 ) |
|
| 7. |
( 1/(sin(X)+cos(X)), X, 0, 2 ) |
(ln(1/ (2)
+ 1) - ln(-1/(2) + 1))/(2) |
| 8. |
( X(1-X2)^(-1/2), X, -1, 0 ) |
-1 |
| 9. |
( (1-X2)^(-1/2), X, -1, 1 ) |
|
| 10. |
( 1/(1-X)2, X, 0, 2 ) |
|
| 11. |
( X+(4-X2),
X, -1, 2 ) |
4/3
+ (3)/2 + 3/2 |
| 12. |
( (R2-X2),
X, 0, R ) |
| Non-Real
ERROR |
<Real
mode> |
| (R2
* signum(R))/4 |
<Complex
mode> |
|
| 13. |
( X ln(X), X, e1, e2 ) |
3e4/4-e2/4 |
| 14. |
( (ln(X))2, X, e1, e2 ) |
2e2-e |
| 15. |
( e (2X) cos(X), X, 0, 1 ) |
-2/(2+4)
- 2 e2 /(2+4) |
| 16. |
( sin(3X)/sin(X), X, /4, /2 ) |
/4
- 1 |
| 17. |
( sin(X)/X, X, -, ) |
|
| 18. |
( X2 ln(X), X, 1, e1 ) |
2e3/9
+ 1/9 |
| 19. |
( (tan(X))^5, X, -/4, /4 ) |
0 |
| 20. |
( (X+X^(1/3)-1)/(X), X ) |
2(X3)/3
+ 66(X5)/5
- 2(X) |
| 21. |
( 2/(X2-9), X ) |
ln(-X+3)/3
- ln(-X-3)/3 |
| 22. |
( 4/(X+1) + (X-3), X ) |
8(X+1)
- 2(X-3) + (2X(X-3))/3 |
| 23. |
( X e(X2+1), X ) |
e(X^2+1)/2 |
| 24. |
( e (3X)/(eX - 1), X ) |
ln(ex
- 1) + (ex )2 /2 + ex |
| 25. |
( (e (3X) + 1)/(eX + 1), X ) |
X
+ (ex )2 /2 - ex |
| 26. |
( 1/(X ln(X)), X ) |
ln(ln(X)) |
| 27. |
( (X) ln(X), X ) |
(2(X3)
ln(X))/3 - 4(X3)/9 |
| 28. |
( ln(X2-1), X ) |
X
ln(X2-1) - 2X - ln(-X+1) + ln(-X-1) |
| 29. |
(
X(1/(1-X2)),
X ) |
-(-X2+1) |
| 30. |
( X/((X+1)+1), X ) |
(2(X+1))/3
+ (2X(X+1))/3 |
| 31. |
( 1/((X+2) - (X)), X ) |
((X3))/3
+ ((4(X+2))/3
+ (2X(X+2))/3)/2 |
| 32. |
( 2X/((X2+1) - X), X ) |
-2X
+ 2 (((X2+1))/3
+ X3/3 + (X2(X2+1))/3
+ X ) |
| 33. |
( 1/(1-X2),
X ) |
sin-1(X) |
| 34. |
( eX sin(X), X ) |
(-ex
cos(X))/2 + (ex sin(X))/2 |
| 35. |
( e(-X) cos(X), X ) |
(-e-x
cos(X))/2 + (e-x sin(X))/2 |
| 36. |
( e (3X) cos(X), X ) |
(3
e3x cos(X))/10 + (e3x sin(X))/10 |
| 37. |
( X/(sin(X))2, X ) |
ln(sin(X))
- X/tan(X) |
| 38. |
( tan(X)/(1-cos(X)), X ) |
-ln(cos(X))
+ ln(-cos(X) + 1) |
| 39. |
( tax(X)/(cos(X))2, X ) |
(tan(X))2/2 |
| 40. |
( sin(ln(X), X ) |
(-X
cos(ln(X)))/2 + (X sin(ln(X)))/2 |
| 41. |
( cos(2X)/(sin(X) - cos(X)), X ) |
cos(X)
- sin(X) |
| 42. |
( X/(cos(X))2, X ) |
ln(cos(X))
+ X tan(X) |
| 43. |
( (tan(X))^3, X ) |
(-ln((tan(X))2
+ 1)/2 + (tan(X))2/2 |
| 44. |
( 1/(cos(X))^4, X ) |
(tan(X))3
/3 + tan(X) |
| 45. |
( sin-1(X) ) |
X
sin-1(X) + (-X2+1) |
| 46. |
( sin(X) e(cos(X)) ) |
-ecos(X) |
| 47. |
( X2 sin(X) ) |
2cos(X)
- X2cos(X) + 2Xsin(X) |
| 48. |
( cos(X) e(sin(X)), X, C ) |
esin(X)
+ C |
| 49. |
( ln(X), X, C ) |
X
ln(X) - X + C |
|
