What is the integral of (3x-2)\sqrt[5]{x} ?

The integral of (3x-2)\sqrt[5]{x} is 15/11 x^{11/5}-5/3 x^{6/5}+C

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integral of (3x-2)\sqrt[5]{x}

\frac{15}{11} x^{\frac{11}{5}} - \frac{5}{3} x^{\frac{6}{5}} + C

Solution steps

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int 3 x^{\frac{6}{5}} d x = \frac{15}{11} x^{\frac{11}{5}}

= \frac{15}{11} x^{\frac{11}{5}} - \frac{5}{3} x^{\frac{6}{5}}

Add a constant to the solution

= \frac{15}{11} x^{\frac{11}{5}} - \frac{5}{3} x^{\frac{6}{5}} + C

y = \frac{2 x}{5 - cot ( x )}

\frac{\partial}{\partial y} (4 x^{2} + 3 y^{4})

x \to 0 lim (\frac{tan ( x ) - x}{x})

\int cot^{2} (3 x) d x

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

What is the integral of (3x-2)\sqrt[5]{x} ?
The integral of (3x-2)\sqrt[5]{x} is 15/11 x^{11/5}-5/3 x^{6/5}+C