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+1 vote
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in Integrals calculus by (36.9k points)

Evaluate: ∫ (4ex + 6e–x / 9ex – 4e–x) dx.

1 Answer

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Best answer

Let 4ex + 6e– x = l(9ex – 6–x ) + m(9ex + 6e– x)

= 4ex + 6e– x = ex (9l + 9m) + e– x (– 6l + 6m)

= 9(l + m) = 4 and – 6 (l – m) = 6

= l = – 5/18, m = 13/18  

Thus,

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