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Popular >

integral of-5e^x+4/x

Solution

\int - 5 e^{x} + \frac{4}{x} d x

Solution

- 5 e^{x} + 4 ln ∣ x ∣ + C

Solution steps

\int - 5 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 5 e^{x} d x + \int \frac{4}{x} d x

\int 5 e^{x} d x = 5 e^{x}

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= - 5 e^{x} + 4 ln ∣ x ∣

Add a constant to the solution

= - 5 e^{x} + 4 ln ∣ x ∣ + C

Popular Examples

derivative of (25/x+(100)/(15-x))

\frac{d}{d x} (\frac{25}{x} + \frac{100}{15 - x})

tangent of x^3-4x tangent of

x^{3} - 4 x

integral of x(a-x)^{5/2}

\int x (a - x)^{\frac{5}{2}} d x

integral of 2/(x^{10)}

\int \frac{2}{x ^{10}} d x

derivative of ln(14*49^x*2^{2x+1})

\frac{d}{d x} (ln (14) \cdot 4 9^{x} \cdot 2^{2 x + 1})

Frequently Asked Questions (FAQ)

What is the integral of-5e^x+4/x ?
The integral of-5e^x+4/x is -5e^x+4ln|x|+C