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ayudenme con esta integral por sustitucion trigonometrica.?
ayuda necesito su ayuda para resolver esta intergral por el metodo de sustitucion trigonométrica.
∫ dx/ (a^2 + X^2)^5/2 si la respuesta a llegar es x / a^2 √(a^2 + x^2) + C
me urge y necesito de su ayuda se los agradeceria mucho.
1 Answer
- Anonymous1 decade agoFavorite Answer
∫ dx/ (a^2 + X^2)^5/2
x = atgθ; dx = asec²θdθ
∫ asec²θdθ/√[a²+ (atgθ)²]⁵
∫ asec²θdθ/√[a²(1+tg²θ)]⁵
∫ asec²θdθ/[a⁵√(sec²θ)⁵]
∫ sec²θdθ/[a⁴sec⁵θ]
1/a⁴ ∫ dθ/sec³θ = 1/a⁴ ∫ cos³θdθ
1/a⁴ ∫ cos²θcosθdθ
1/a⁴ ∫ (1-sen²θ)cosθdθ
1/a⁴ ∫ [cosθdθ-3sen²θcosθdθ/3]
1/a⁴ [senθdθ-sen³θ/3]
Hipotenusa =(a^2 + X^2)^(1/2)
senθ = x/[a(a^2 + X^2)^(1/2)]
1/a⁴ {x /[a√(a²+x²)] - x³ / [3a³√(a²+x²)³]}
x /[a⁵√(a²+x²)] - x³ / [3a⁷√(a²+x²)³]