Techniques of Integration · Trigonometric Methods
Trig Integrals: secᵐx tanⁿx
Strategy: If n is odd, save sec x tan x and convert tan² = sec²-1. If m is even, save sec²x and convert sec² = 1+tan².
- 0 variables
- 2 worked examples
- 16 in Techniques of Integration
Worked examples
Find ∫ sec⁴x tan²x dx.
- m = 4 is even. Save sec²x: ∫ sec²x tan²x sec²x dx
- sec²x = 1+tan²x: ∫ (1+tan²x) tan²x sec²x dx
- u = tanx, du = sec²x dx: ∫ (1+u²)u² du = ∫ (u²+u⁴) du
- = u³/3 + u⁵/5 + C = tan³x/3 + tan⁵x/5 + C
Answer: tan³x/3 + tan⁵x/5 + C
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Find ∫ sec³x tan x dx.
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Practice
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