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

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

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

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

- 3 e^{x} + 4 ln ∣ x ∣ + C

Solution steps

\int - 3 e^{x} + \frac{4}{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 \frac{4}{x} d x

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= - 3 e^{x} + 4 ln ∣ x ∣

Add a constant to the solution

= - 3 e^{x} + 4 ln ∣ x ∣ + C

\int_{7}^{8} e^{7 - x} d x

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

\int 2 x x^{2} + 1 d x

2 y^{^{''}} - 54 y = 0, y (1) = 1, y (2) = 2

x \to 0 lim (x (ln (x)))

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