What is the integral of (x^2+sqrt(x)+1/x) ?

The integral of (x^2+sqrt(x)+1/x) is (x^3)/3+2/3 x^{3/2}+ln|x|+C

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integral of (x^2+sqrt(x)+1/x)

\int (x^{2} + x + \frac{1}{x}) d x

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

Solution steps

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

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

Add a constant to the solution

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

f (x) = 5 x^{2} - 5 x + 9

\frac{d}{d x} (- 9 x^{3} + 27 x + 7 x - 66)

3 x, at x = 4

\int 5 tan^{3} (x) sec^{3} (x) d x

\int_{1}^{4} \frac{1}{x} d x

What is the integral of (x^2+sqrt(x)+1/x) ?
The integral of (x^2+sqrt(x)+1/x) is (x^3)/3+2/3 x^{3/2}+ln|x|+C