What is the integral of x^{2/3}+x ?

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

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integral of x^{2/3}+x

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

\frac{3}{5} x^{\frac{5}{3}} + \frac{x ^{2}}{2} + C

Solution steps

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

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

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

= \frac{3}{5} x^{\frac{5}{3}} + \frac{x ^{2}}{2}

Add a constant to the solution

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

\int_{- 6}^{5} x^{2} - 3 x - 4 d x

cos^{2} (x)

\int \frac{x ^{2}}{( x ^{2} + 16 ) ^{\frac{3}{2}}} d x

\frac{\partial}{\partial x} (\frac{6 x}{y ^{2}})

\frac{1}{10 \cdot s}

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