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

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

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integral of (sqrt(x)+1/x+sqrt(pi))

\int (x + \frac{1}{x} + π) d x

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

Solution steps

\int x + \frac{1}{x} + π 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 d x + \int \frac{1}{x} d x + \int π d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int π d x = π x

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

Add a constant to the solution

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

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\int tan (θ) ln (sec (θ)) d θ

\frac{d r}{d s} = e^{r - 7 s}

\int [3 sin (x) + (\frac{1}{2}) tan (x)] d x

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