If ∫ 4 e x − 5 e − x 3 e x + 5 e − x d x = A x + B ln 4 e 2 x − 5 + C , which statements are true?

Question

If ∫ 4 e x − 5 e − x 3 e x + 5 e − x ​ d x = A x + B ln ​ 4 e 2 x − 5 ​ + C , which statements are true?

TestHub · Accepted Answer

Decomposition gives − 1 + 8 7 ​ 4 e 2 x − 5 8 e 2 x ​ after multiplying numerator and denominator appropriately. Integration yields − x + 8 7 ​ ln ​ 4 e 2 x − 5 ​ + C . The integration constant is arbitrary.

Mathematics - Indefinite Integration Question with Solution | TestHub

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