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Integration by Parts, Partial Fractions and Special Integrals
Mathematics · Chapter 9 · Unit 3: Calculus
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Your path through this chapter
Visual lesson Beta
- Part 1: Integration by Parts and Partial Fractions — Part 118 slides
- Part 2: Quadratics, roots, trigonometric forms18 slides
Flashcards Beta
30 cards for quick recall of key terms and facts.
Review the cards Step 3: Not startedPractice
70 board-style questions with instant checks: Multiple choice 26, Short answer 19, Assertion and reason 7, Long answer 6.
Practise Step 4: Not startedChapter test Free
Short and long chapter tests in board pattern, with results and analysis.
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Topics 6
- Integration by parts
- Partial fractions for proper rational functions (linear, repeated linear and quadratic factors) and improper ones
- Integrals of dx/(x^2 +- a^2), dx/(a^2 - x^2), dx/sqrt(x^2 +- a^2), dx/(ax^2 + bx + c), (px + q)/(ax^2 + bx + c) and their square-root forms
- Integrals of sqrt(a^2 - x^2), sqrt(x^2 - a^2), sqrt(ax^2 + bx + c) and (px + q) sqrt(ax^2 + bx + c)
- Trigonometric forms: dx/(a + b cos x), dx/(a + b sin x), dx/(a cos x + b sin x + c), (c cos x + d sin x)/(a cos x + b sin x), dx/(a cos^2 x + b sin^2 x + c)
- Special integrals such as (1 +- x^2)/(1 + x^4), sqrt(tan x) and sqrt(cot x)