What is the integral of e-xcos(2x) ?

The integral of e-xcos(2x) is ex-1/4 (2xsin(2x)+cos(2x))+C

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integral of e-xcos(2x)

\int e - x cos (2 x) d x

e x - \frac{1}{4} (2 x sin (2 x) + cos (2 x)) + C

Solution steps

\int e - x cos (2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e d x - \int x cos (2 x) d x

\int e d x = e x

\int x cos (2 x) d x = \frac{1}{4} (2 x sin (2 x) + cos (2 x))

= e x - \frac{1}{4} (2 x sin (2 x) + cos (2 x))

Add a constant to the solution

= e x - \frac{1}{4} (2 x sin (2 x) + cos (2 x)) + C

\int \frac{e ^{a x + b} - e ^{b x + a}}{e ^{a x}} d x

- 9 y^{^{''}} + 81 y = 0

n = 0 \sum \infty \frac{( 2 ^{n} )}{n !}

\frac{28}{( s ^{2} + 11 )}

x \to 1 lim (3 x^{4} + 3 x^{2} - x + 2)

What is the integral of e-xcos(2x) ?
The integral of e-xcos(2x) is ex-1/4 (2xsin(2x)+cos(2x))+C