What is the integral of (e^{2x}+sin(2x)) ?

The integral of (e^{2x}+sin(2x)) is 1/2 e^{2x}-1/2 cos(2x)+C

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integral of (e^{2x}+sin(2x))

\int (e^{2 x} + sin (2 x)) d x

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

Solution steps

\int e^{2 x} + sin (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^{2 x} d x + \int sin (2 x) d x

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

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

= \frac{1}{2} e^{2 x} - \frac{1}{2} cos (2 x)

Add a constant to the solution

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

\frac{d}{d x} (sin (x) + \frac{8}{3} cot (x))

\frac{d}{d x} (\frac{1}{2} x + 1)

\frac{d}{d x} (\frac{9 x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

\frac{d}{d x} (\frac{x ^{5} - 5 x}{5})

\int \frac{x}{a + b x ^{2}} d x

What is the integral of (e^{2x}+sin(2x)) ?
The integral of (e^{2x}+sin(2x)) is 1/2 e^{2x}-1/2 cos(2x)+C