What is the integral of (-5e^x+4/x) ?

The integral of (-5e^x+4/x) is -5e^x+4ln|x|+C

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integral of (-5e^x+4/x)

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

- 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

\frac{d}{d y} (x y^{2})

\int t sin (k t) d t

\int \frac{1}{y ^{2} y ^{2} + 16} d y

d er i v a t i v e 4 x^{\frac{5}{4}} + 10 x^{\frac{3}{2}} + 8 x

x \to 0 - lim ((1 + x)^{\frac{1}{x ^{2}}})

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