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

The integral of (3/x-9e^{5x}+sqrt(x^9)) is 3ln|x|-9/5 e^{5x}+2/11 x^{11/2}+C

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

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

3 ln ∣ x ∣ - \frac{9}{5} e^{5 x} + \frac{2}{11} x^{\frac{11}{2}} + C

Solution steps

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 9 e^{5 x} d x = \frac{9}{5} e^{5 x}

\int x^{9} d x = \frac{2}{11} x^{\frac{11}{2}}

= 3 ln ∣ x ∣ - \frac{9}{5} e^{5 x} + \frac{2}{11} x^{\frac{11}{2}}

Add a constant to the solution

= 3 ln ∣ x ∣ - \frac{9}{5} e^{5 x} + \frac{2}{11} x^{\frac{11}{2}} + C

What is the integral of (3/x-9e^{5x}+sqrt(x^9)) ?
The integral of (3/x-9e^{5x}+sqrt(x^9)) is 3ln|x|-9/5 e^{5x}+2/11 x^{11/2}+C