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oivanovml2008
@oivanovml2008
July 2022
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Помогите решить с помощью замены
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TARTILLO
Verified answer
∫[∛(ln(3x+1))/(3x+1)] dx=
I t=ln(3x+1) dt=[1/(3x+1)]3dx I ⇔
∫[∛(ln(3x+1))/(3x+1)] dx=(1/3)∫∛t dt =(1/3)·[ t^(1/3+1)] /(1/3+1)+C=[t^(4/3)]/4+C=
{ln(3x+1)]^(4/3)}/4+C
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Answers & Comments
Verified answer
∫[∛(ln(3x+1))/(3x+1)] dx=I t=ln(3x+1) dt=[1/(3x+1)]3dx I ⇔
∫[∛(ln(3x+1))/(3x+1)] dx=(1/3)∫∛t dt =(1/3)·[ t^(1/3+1)] /(1/3+1)+C=[t^(4/3)]/4+C=
{ln(3x+1)]^(4/3)}/4+C