What is the integral of (9-5e^x+3/(x^2)) ?

The integral of (9-5e^x+3/(x^2)) is 9x-5e^x-3/x+C

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integral of (9-5e^x+3/(x^2))

\int (9 - 5 e^{x} + \frac{3}{x ^{2}}) d x

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

Solution steps

\int 9 - 5 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 9 d x - \int 5 e^{x} d x + \int \frac{3}{x ^{2}} d x

\int 9 d x = 9 x

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

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

= 9 x - 5 e^{x} - \frac{3}{x}

Add a constant to the solution

= 9 x - 5 e^{x} - \frac{3}{x} + C

What is the integral of (9-5e^x+3/(x^2)) ?
The integral of (9-5e^x+3/(x^2)) is 9x-5e^x-3/x+C