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el bueno
Lv 5
el bueno asked in Ciencias y matemáticasMatemáticas · 1 decade ago

ayudenme con esta integral trigonométrica ¡¡¡¡?

∫((cos^3 x)/(sen^4 x)) dx y la respuesta es = cosec x - 1/3 cosec^3 x + C

necesito el procedimiento completo y agradeceria su ayuda.

1 Answer

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  • railrule
    Lv 7
    1 decade ago
    Favorite Answer

    hola

    cos x dx = d (sen x)

    u = sen x

    cos x dx = d u

    cos^2 x = 1 - sen^2 x = 1 - u^2

    I = int [(1 - u^2)/u^4] du

    I = int [(1/u^4) - (1/u^2)] du

    I = int [(u^-4) - (u^-2)] du

    I = - (u^-3)/3 + (u^1)/1 + K

    I = cosec x - (1/3) cosec^3 x + k

    saludos

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