What is the integral of (4\sqrt[3]{x}-2xsqrt(x)) ?

The integral of (4\sqrt[3]{x}-2xsqrt(x)) is 3x^{4/3}-4/5 x^{5/2}+C

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integral of (4\sqrt[3]{x}-2xsqrt(x))

\int (4 3 x - 2 x x) d x

3 x^{\frac{4}{3}} - \frac{4}{5} x^{\frac{5}{2}} + C

Solution steps

\int 4 3 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 4 3 x d x - \int 2 x x d x

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

\int 2 x x d x = \frac{4}{5} x^{\frac{5}{2}}

= 3 x^{\frac{4}{3}} - \frac{4}{5} x^{\frac{5}{2}}

Add a constant to the solution

= 3 x^{\frac{4}{3}} - \frac{4}{5} x^{\frac{5}{2}} + C

\frac{d}{d t} (7 cos (t))

x \to - 5 + lim (\frac{x + 4}{x + 5})

\int_{0}^{2} 4 x - 2 x^{2} d x

l a pl a ce t r an s f or m t + sin (t)

l a pl a ce t r an s f or m sin (2 t) cos (5 t)

What is the integral of (4\sqrt[3]{x}-2xsqrt(x)) ?
The integral of (4\sqrt[3]{x}-2xsqrt(x)) is 3x^{4/3}-4/5 x^{5/2}+C