What is the integral of x^{-1}+x^{1/3}+5/3 ?

The integral of x^{-1}+x^{1/3}+5/3 is ln|x|+3/4 x^{4/3}+5/3 x+C

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integral of x^{-1}+x^{1/3}+5/3

\int x^{- 1} + x^{\frac{1}{3}} + \frac{5}{3} d x

ln ∣ x ∣ + \frac{3}{4} x^{\frac{4}{3}} + \frac{5}{3} x + C

Solution steps

\int x^{- 1} + x^{\frac{1}{3}} + \frac{5}{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 x^{- 1} d x + \int x^{\frac{1}{3}} d x + \int \frac{5}{3} d x

\int x^{- 1} d x = ln ∣ x ∣

\int x^{\frac{1}{3}} d x = \frac{3}{4} x^{\frac{4}{3}}

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

= ln ∣ x ∣ + \frac{3}{4} x^{\frac{4}{3}} + \frac{5}{3} x

Add a constant to the solution

= ln ∣ x ∣ + \frac{3}{4} x^{\frac{4}{3}} + \frac{5}{3} x + C

x \to - 1 lim (x^{2} + 4 x + 3)

\frac{d}{d x} (\frac{1}{2} x^{- \frac{1}{2}})

\int 50 - 6.3 e^{0.9 x} d x

\int (3 x + 2)^{5} d x

\frac{d}{d x} (e^{2 x^{4}})

What is the integral of x^{-1}+x^{1/3}+5/3 ?
The integral of x^{-1}+x^{1/3}+5/3 is ln|x|+3/4 x^{4/3}+5/3 x+C