I-cosx-2sinx-e-2x-sinx-dx-

Question Number 150932 by maged last updated on 16/Aug/21

I = \int \frac{cosx - 2 sinx}{e^{2 x} - sinx} dx \overset{?}{=}

Answered by Olaf_Thorendsen last updated on 16/Aug/21

F (x) = \int \frac{\cos x - 2 \sin x}{e^{2 x} - \sin x} d x

F (x) = \int \frac{(2 e^{2 x} - 2 \sin x) - (2 e^{2 x} - \cos x)}{e^{2 x} - \sin x} d x

F (x) = \int (2 - \frac{2 e^{2 x} - \cos x}{e^{2 x} - \sin x}) d x

F (x) = 2 x - \ln ∣ e^{2 x} - \sin x ∣ + C

Commented by maged last updated on 16/Aug/21

Thank you

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