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

The integral of 2/x+3sin(x)-4e^x is 2ln|x|-3cos(x)-4e^x+C

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integral of 2/x+3sin(x)-4e^x

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

2 ln ∣ x ∣ - 3 cos (x) - 4 e^{x} + C

Solution steps

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 3 sin (x) d x = - 3 cos (x)

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

= 2 ln ∣ x ∣ - 3 cos (x) - 4 e^{x}

Add a constant to the solution

= 2 ln ∣ x ∣ - 3 cos (x) - 4 e^{x} + C

\frac{\partial}{\partial x} (6 z e^{x yz})

y^{^{'}} = 20 - 4 y

e^{- 43 t} \cdot e^{72 t} cos (77 t)

\int 5 sin (\frac{x}{4}) d x

\frac{d}{d s} (\frac{1}{s ^{2}})

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