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Popular >

integral of 2/x-4e^x

Solution

\int \frac{2}{x} - 4 e^{x} d x

Solution

2 ln ∣ x ∣ - 4 e^{x} + C

Solution steps

\int \frac{2}{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 4 e^{x} d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ - 4 e^{x}

Add a constant to the solution

= 2 ln ∣ x ∣ - 4 e^{x} + C

Graph

Popular Examples

(\partial)/(\partial x)((3y)/(x^5))

\frac{\partial}{\partial x} (\frac{3 y}{x ^{5}})

integral from 2 to infinity of e^{-x/3}

\int_{2}^{\infty} e^{- \frac{x}{3}} d x

derivative of cos(sin(x^3))derivative of

cos (sin (x^{3}))

y^3-(18x+4)+3xy^2y^'=0

y^{3} - (18 x + 4) + 3 x y^{2} y^{^{'}} = 0

(\partial)/(\partial x)(e^{-x}*(x-y^2))

\frac{\partial}{\partial x} (e^{- x} \cdot (x - y^{2}))

Frequently Asked Questions (FAQ)

What is the integral of 2/x-4e^x ?
The integral of 2/x-4e^x is 2ln|x|-4e^x+C