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kit9kit123
@kit9kit123
July 2022
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2 номер . Интегралы. ПОМОГИТЕ
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Gerren
∫((a+b/(x-a))^2)dx
u=x-a du=dx
∫((a+b/(x-a))^2)dx=∫(a+b/u)^2du=∫(a^2+2ab/u+(b/u)^2)du=∫a^2du+∫(2ab/u)du+∫(b/u)^2)du=(a^2)u^2/2+2ablnu-b/u+C
Делаем возврат
(a^2)(x-a)+2abln(x-a)-b/(x-a)+C
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Answers & Comments
u=x-a du=dx
∫((a+b/(x-a))^2)dx=∫(a+b/u)^2du=∫(a^2+2ab/u+(b/u)^2)du=∫a^2du+∫(2ab/u)du+∫(b/u)^2)du=(a^2)u^2/2+2ablnu-b/u+C
Делаем возврат
(a^2)(x-a)+2abln(x-a)-b/(x-a)+C