What is the integral of 3e^x+5sin(x) ?

The integral of 3e^x+5sin(x) is 3e^x-5cos(x)+C

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integral of 3e^x+5sin(x)

\int 3 e^{x} + 5 sin (x) d x

3 e^{x} - 5 cos (x) + C

Solution steps

\int 3 e^{x} + 5 sin (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 3 e^{x} d x + \int 5 sin (x) d x

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

\int 5 sin (x) d x = - 5 cos (x)

= 3 e^{x} - 5 cos (x)

Add a constant to the solution

= 3 e^{x} - 5 cos (x) + C

y = (x^{3} - 25 x)^{8}, (5, 0)

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

\frac{d y}{d x}, x = cos (2 y)

x \to 0 lim (\frac{5}{2} x^{2})

\int sin (x) sin (\frac{2 x}{3}) d x

What is the integral of 3e^x+5sin(x) ?
The integral of 3e^x+5sin(x) is 3e^x-5cos(x)+C