Stewart Calculus Section 7.5

1. 7.5 Strategy for
Integration
Integration need to be memorized:
√ √
− + ± −
Integration need to know how to derive:

2. Ex:

3. Ex:
+
=

4. Ex:
+
=
= +

5. Ex:
+
=
= +
= +

6. Ex:
+
=
= +
= +
=
( / )

7. Ex:
+
=
= +
= +
=
( / )
= ( / )+

8. Ex:

9. Ex:
=

10. Ex:
=
=

11. Ex:
=
=
= +

12. Ex:
=
=
= +
=

13. Ex:
=
=
= +
=
=

14. Ex:
=
=
= +
=
=
= +

15. Ex:
+

16. Ex:
+
= =
+ ( + ) +

17. Ex:
+
= =
+ ( + ) +
+ +
= +
+ ( + )

18. Ex:
+
= =
+ ( + ) +
+ +
= +
+ ( + )
= +
+ ( + )

19. Ex:
+
= =
+ ( + ) +
+ +
= +
+ ( + )
= +
+ ( + )
=
+

20. Ex:
+
= =
+ ( + ) +
+ +
= +
+ ( + )
= +
+ ( + )
=
+
= + +

21. Elementary function:
polynomials, rational func., power func., exp
func., log func., tri. and inverse tri. func.,
hyperbolic and inverse hyperbolic func., and
their addition, subtraction, multiplication,
division and compositions.

22. Elementary function:
polynomials, rational func., power func., exp
func., log func., tri. and inverse tri. func.,
hyperbolic and inverse hyperbolic func., and
their addition, subtraction, multiplication,
division and compositions.
The antiderivative of an elementary function is
not necessarily elementary.
( ) +