What is the integral of 5x^{1/3}+2x^{-1/3}+11 ?

The integral of 5x^{1/3}+2x^{-1/3}+11 is 15/4 x^{4/3}+3x^{2/3}+11x+C

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integral of 5x^{1/3}+2x^{-1/3}+11

\int 5 x^{\frac{1}{3}} + 2 x^{- \frac{1}{3}} + 11 d x

\frac{15}{4} x^{\frac{4}{3}} + 3 x^{\frac{2}{3}} + 11 x + C

Solution steps

\int 5 x^{\frac{1}{3}} + 2 x^{- \frac{1}{3}} + 11 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 5 x^{\frac{1}{3}} d x + \int 2 x^{- \frac{1}{3}} d x + \int 11 d x

\int 5 x^{\frac{1}{3}} d x = \frac{15}{4} x^{\frac{4}{3}}

\int 2 x^{- \frac{1}{3}} d x = 3 x^{\frac{2}{3}}

\int 11 d x = 11 x

= \frac{15}{4} x^{\frac{4}{3}} + 3 x^{\frac{2}{3}} + 11 x

Add a constant to the solution

= \frac{15}{4} x^{\frac{4}{3}} + 3 x^{\frac{2}{3}} + 11 x + C

\int \frac{x + 1}{x ^{2} - 4 x + 8} d x

\int_{- 1}^{2} (2 - y^{2}) - (- y) d y

n = 0 \sum \infty 10 (\frac{1}{3})^{n}

(\frac{x + 5}{x ^{2} + 2})^{2}

What is the integral of 5x^{1/3}+2x^{-1/3}+11 ?
The integral of 5x^{1/3}+2x^{-1/3}+11 is 15/4 x^{4/3}+3x^{2/3}+11x+C