What is the integral of (5-4e^x+3/(x^2)) ?

The integral of (5-4e^x+3/(x^2)) is 5x-4e^x-3/x+C

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integral of (5-4e^x+3/(x^2))

\int (5 - 4 e^{x} + \frac{3}{x ^{2}}) d x

5 x - 4 e^{x} - \frac{3}{x} + C

Solution steps

\int 5 - 4 e^{x} + \frac{3}{x ^{2}} 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 d x - \int 4 e^{x} d x + \int \frac{3}{x ^{2}} d x

\int 5 d x = 5 x

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

\int \frac{3}{x ^{2}} d x = - \frac{3}{x}

= 5 x - 4 e^{x} - \frac{3}{x}

Add a constant to the solution

= 5 x - 4 e^{x} - \frac{3}{x} + C

h \to 0 lim (\frac{( 2 h ^{2} + 6 h )}{h})

x \to 0 lim (f (x) \cdot g (x))

\frac{d}{d x} (\frac{- x ^{2}}{4})

f (x) = (4 z^{4} + 2 z^{2} + 1) (2 z^{3} - z)

\int - \frac{1}{2 x + 1} d x

What is the integral of (5-4e^x+3/(x^2)) ?
The integral of (5-4e^x+3/(x^2)) is 5x-4e^x-3/x+C