| Integrál
(CAS) |
| Popis funkce |
| vypočte integrál funkce |
| Zadání |
| [F2](CALC)[2](∫) |
| Syntaxe |
∫
(výraz , proměnná )
∫ (výraz , proměnná , dolní mez , horní mez
, integrační konstanta
∫ (výraz , proměnná
, integrační konstanta )
* pokud není proměnná zadána, je za ní považováno
X |
| Příklad |
| 1. |
|
vypočti integrál X2 pro proměnou 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, 2p
) |
(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 ) |
p |
| 10. |
|
∫ (
1/(1-X)2, X, 0, 2 ) |
∞ |
| 11. |
|
∫ (
X+√(4-X2), X, -1, 2 ) |
4p/3 + √ (3)/2 + 3/2 |
| 12. |
|
∫ (
√(R2-X2), X, 0, R ) |
Non-Real ERROR
<reálná čísla>
(pR2 * signum(R))/4
<komplexní čísla> |
| 13. |
|
∫
( X ln(X), X, e1, e2 ) |
3e4/4-e2/4 |
| 14. |
|
∫ (
(ln(X))2, X, e1, e2 ) |
2e2-e |
| 15. |
|
∫ ( e(2X)
cos(pX), X, 0, 1 ) |
-2/(p2+4) - 2
e2 /(p2+4) |
| 16. |
|
∫ ( sin(3X)/sin(X), X,
p/4, p/2 ) |
p/4 - 1 |
| 17. |
|
∫ ( sin(X)/X, X,
-∞,
∞ ) |
p |
| 18. |
|
∫ ( X2 ln(X), X, 1, e1 ) |
2e3/9 + 1/9 |
| 19. |
|
∫ ( (tan(X))^5, X,
-p/4, p/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 |
|
|
|
