What is the integral of x(\sqrt[3]{x}+sqrt(x)+1) ?

The integral of x(\sqrt[3]{x}+sqrt(x)+1) is 3/7 x^{7/3}+2/5 x^{5/2}+(x^2)/2+C

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integral of x(\sqrt[3]{x}+sqrt(x)+1)

\frac{3}{7} x^{\frac{7}{3}} + \frac{2}{5} x^{\frac{5}{2}} + \frac{x ^{2}}{2} + C

Solution steps

Expand

= \int x^{\frac{4}{3}} + x^{\frac{3}{2}} + 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{4}{3}} d x + \int x^{\frac{3}{2}} d x + \int x d x

\int x^{\frac{4}{3}} d x = \frac{3}{7} x^{\frac{7}{3}}

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

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

= \frac{3}{7} x^{\frac{7}{3}} + \frac{2}{5} x^{\frac{5}{2}} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{3}{7} x^{\frac{7}{3}} + \frac{2}{5} x^{\frac{5}{2}} + \frac{x ^{2}}{2} + C

f (x) = sin (x) ln (x^{2} + 1)

x \to π lim (9 cot (x))

y = ln (x^{6})

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

\int \frac{1 + sin ( x )}{x ^{3}} d x

What is the integral of x(\sqrt[3]{x}+sqrt(x)+1) ?
The integral of x(\sqrt[3]{x}+sqrt(x)+1) is 3/7 x^{7/3}+2/5 x^{5/2}+(x^2)/2+C