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

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

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

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

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

Solution steps

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

\int sin (3 x) d x = - \frac{1}{3} cos (3 x)

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

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

Add a constant to the solution

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

\int (\frac{x sin ^{2} ( x )}{2}) d x

x \to 0 + lim (x^{(x^{2})})

h \to 0 lim (h^{2})

10 t^{3}

f (x) = 2 x^{2} + 7 x, at x = 4

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