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

The integral of 9+e^{2x}-5/(x^3) is 9x+1/2 e^{2x}+5/(2x^2)+C

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

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

9 x + \frac{1}{2} e^{2 x} + \frac{5}{2 x ^{2}} + C

Solution steps

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

\int 9 d x = 9 x

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

\int \frac{5}{x ^{3}} d x = - \frac{5}{2 x ^{2}}

= 9 x + \frac{1}{2} e^{2 x} - (- \frac{5}{2 x ^{2}})

Simplify

= 9 x + \frac{1}{2} e^{2 x} + \frac{5}{2 x ^{2}}

Add a constant to the solution

= 9 x + \frac{1}{2} e^{2 x} + \frac{5}{2 x ^{2}} + C

What is the integral of 9+e^{2x}-5/(x^3) ?
The integral of 9+e^{2x}-5/(x^3) is 9x+1/2 e^{2x}+5/(2x^2)+C