This document discusses integration using u-substitutions. It covers power rule integration, trigonometric integration, integrands, and separable differential equations. Specific topics include finding derivatives using the power rule, calculating derivatives and integrals of trigonometric functions, odd and even integrands, and solving separable differential equations. Worked examples and frequently asked questions are provided for each topic.

1. Integration using u-substitutions

2. Integration using u-substitutions
posted on: 18 Jan, 2012 | updated on: 26 Jul, 2012
Topics Covered in Integration using u-substitutions
Power rule | Integration Power Rule
Trigonometric | Trigonometric Integration
Integrands | Integration Calculus
Separable Equations | Separable Differential equation

3. Power rule
posted on: 06 Feb, 2012 | updated on: 24 May, 2012
Find d/dx of (x2) using power rule?

4. Determine the function d/dx (-1/x) using power rule?

5. Determine the function d/dx (-3x2) using power rule?

6. Evaluate the function d/dx (4x - x3) using power rule?

7. Find the derivatives of the function y = 7x5 usingpower rule?

8. Find the derivatives of the function y = 10x3 using power rule?

9. Find the derivatives of the function y = -1/2 x3 using power rule?

10. Find the derivatives of the function y = 100 x6 using power rule?

11. Determine the derivatives of the function y = x200 using power
rule?

12. Evaluate the function y = (5 + 10x4)using power rule?

13. Find the function y = (-x2 – x7)using power rule?

14. Trigonometric
posted on: 06 Feb, 2012 | updated on: 26 Jul, 2012

15. Calculate differentiation of the following function f (x) where f (x)
= [sin (x) - x cos(x)] / [x sin(x) + cos(x)]?
Calculate Differentiation of the following function f (x) where f (x)
= 2x cot (x) / ?x?

16. Calculate Differentiation of the following function f (x) where
f (x) = ex + sin (x) / [ 1 + log (x) ] ?

17. Calculate Differentiation of the following function f (x) where
f (x) = [ ex.tan (x).log (?x) ]?

18. Calculate Differentiation of the following function f (x) where
f (x) = [ cos (x) / [ 1 + sin (x) ] ?

19. Calculate Integration of the following function f (x) where f (x) =
[cos (3 x)]?

20. Calculate Integration of the following function f (x) where
f (x) = [ x . sin (3x)] ?

21. Calculate Integration of the following function f (x) where
f (x) = [arc cos (3x)]?

22. Calculate Integration of the following function f (x) where f (x) = [
sin (x) + cos (x)]?

23. Calculate Integration of the following function f (x) where f (x) =
[2x . arc sin (x)]?

24. Integrands
posted on: 06 Feb, 2012 | updated on: 23 Jul, 2012

25. FAQ of Integrands | Integration Calculus
Odd Integrands
Separable Differential equations
posted on: 06 Feb, 2012 | updated on: 24 May, 2012
Solve the separable differential equation 2x dx = (y2 +1) dy?

26. Find the separable differential equation of function x dx + sin x
cos y dy = 0?

27. Find the separable differential equation of function y dy + tan x
cos y dx = 0?

28. Find the separable differential equation of function x2 +5 dx + cos
x cos y dy = 0?

29. FAQ of Separable Equations | Separable Differential equation
Solve the given differential equation by separation of variables?

30. Further Read
Integration using u-substitutions Examples
Integration using u-substitutions FAQs
Integration using u-substitutions Worksheets
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