What is the integral of 3/x+x^2-sqrt(x^3) ?

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

integral of 3/x+x^2-sqrt(x^3)

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

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

Solution steps

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

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

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

Add a constant to the solution

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

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