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

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

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integral of \sqrt[5]{x^2}+xsqrt(x)

\int 5 x^{2} + x x d x

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

Solution steps

\int 5 x^{2} + 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 5 x^{2} d x + \int x x d x

\int 5 x^{2} d x = \frac{5}{7} x^{\frac{7}{5}}

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

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

Add a constant to the solution

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

\frac{s}{s ^{2} + 3 s + 1}

n = 0 \sum \infty \frac{n !}{e ^{n}}

\int x^{3} + 1 d x

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

\frac{d}{d x} (\frac{x ^{2} + 7}{x - 3})

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