What is the integral of sin(2x)-4e^{3x} ?

The integral of sin(2x)-4e^{3x} is -1/2 cos(2x)-4/3 e^{3x}+C

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integral of sin(2x)-4e^{3x}

\int sin (2 x) - 4 e^{3 x} d x

- \frac{1}{2} cos (2 x) - \frac{4}{3} e^{3 x} + C

Solution steps

\int sin (2 x) - 4 e^{3 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 sin (2 x) d x - \int 4 e^{3 x} d x

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

\int 4 e^{3 x} d x = \frac{4}{3} e^{3 x}

= - \frac{1}{2} cos (2 x) - \frac{4}{3} e^{3 x}

Add a constant to the solution

= - \frac{1}{2} cos (2 x) - \frac{4}{3} e^{3 x} + C

n = 2 \sum \infty \frac{1}{n ^{2} + 4 n}

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

y^{^{'}} = \frac{x y}{2}

\int_{0}^{1} x^{4} e^{5 x} d x

\int a tan^{2} (θ) d θ

What is the integral of sin(2x)-4e^{3x} ?
The integral of sin(2x)-4e^{3x} is -1/2 cos(2x)-4/3 e^{3x}+C