What is the integral of \sqrt[7]{x^2}+xsqrt(x) ?

The integral of \sqrt[7]{x^2}+xsqrt(x) is 7/9 x^{9/7}+2/5 x^{5/2}+C

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integral of \sqrt[7]{x^2}+xsqrt(x)

\frac{7}{9} x^{\frac{9}{7}} + \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

assuming

x \geq 0

= \int x^{\frac{2}{7}} + x 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}{7}} d x + \int x x d x

\int x^{\frac{2}{7}} d x = \frac{7}{9} x^{\frac{9}{7}}

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

= \frac{7}{9} x^{\frac{9}{7}} + \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{7}{9} x^{\frac{9}{7}} + \frac{2}{5} x^{\frac{5}{2}} + C

y = x^{2} + 4 x + 3

n = 0 \sum \infty sin (\frac{1}{n ^{2}})

x \to 0 lim (\frac{\frac{1}{1 + x} - 1}{x})

ln (3 - x^{3})

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

What is the integral of \sqrt[7]{x^2}+xsqrt(x) ?
The integral of \sqrt[7]{x^2}+xsqrt(x) is 7/9 x^{9/7}+2/5 x^{5/2}+C