Indefinite IntegrationHard

Question

If ∫ e3x cos 4x dx = e3x (A sin 4x + B cos 4x) + C then:

Options

A.4A = 3B
B.2A = 3B
C.3A = 4B
D.4A + 3B = 1

Solution

I = ∫e3x cos4x dx = e3x(Asin4x + Bcos4x) + C   .....(i)
I = e3x sin 4x -
= e3x sin4x + e3xcos4x - dx
(4e3x sin4x + 3e3x cos4x)
comparing with equation (i)
⇒ A =     ⇒        ⇒   3A = 4B   ⇒    4A + 3B = 1

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