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Answer on Calculus Question for Akhtar Rasool khan

Question #5340
Respect Sir pease help me to choose which function first using integration by parts in logarithm and inverse functions . for example"Integral logx.sin inverse x"dx
Expert's answer
Integrals of this type are expressed in terms of special functions. It is impossible to express the answer in terms of elementary functions. Integration by parts does not work.
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" 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